Prof. Vakhtang Kokilashvili

(1.V.1938 - 16.V.2022)

 

Education

Institution

Learning Time

Secondary

Tbilisi Secondary School N 7

1948-1954

Higher

Faculty of Mechanics and Mathematics

1954-1959

Postgraduate study, doctoral candidacy

Postgraduate study, A. Razmadze Mathematical Institute of Georgian Academy of Sciences

1959-1962


Knowledge of Languages

Foreign languages

Level of language proficiency (fluent, intermediate, beginning with the help of a dictionary)

English

Free

Germany

with help of dictionary

Russian

Free

 

Scientific or Academic Degree and Rank

 

Title of the thesis

Date of conferment

Ph.D. thesis

On the coefficients of Fourier trigonometric series, approximation of functions

1963

Doctoral thesis

Singular integrals weighted Lizorkin-Triebel spaces, imbedding theorems

1981

Academician Doctor

 

 

Professor

 

1985

Corresponding Member (Academician) of the Georgian National Academy of Sciences

 

1997

Full Member (Academician) of the Georgian National Academy of Sciences

 

2013

 
Work Experience

Date

Institution

Position

1963-1966

A. Razmadze Mathematical Institute

Researcher

1966-1986

A. Razmadze Mathematical Institute

Senior  Researcher

1986-2001

A. Razmadze Mathematical Institute

Leading Researcher

2001-2022

A. Razmadze Mathematical Institute

Main  Researcher

1990-2022

A. Razmadze Mathematical Institute

Head of Department of Complex Analysis, then Mathematical Analysis

1989-2006

A. Razmadze Mathematical Institute

Vice Director

2006 2022

I. Javakhishvili Tbilisi State Universiry, A. Razmadze Mathematical Institute

Head of Mathematical Analysis Department


Teaching Activity

Date

Institution

Position

1966-1985

I. Javakhishvili Tbilisi State University

Docent

1985-2005

I. Javakhishvili Tbilisi State University

Professor

2009-2012

I. Javakhishvili Tbilisi State University

Invited Lecturer

2006-2009

Telavi I. Gogebashvili State University

Full  Professor

1996-2006

Sukhumi Branch of  I. Javakhishvili Tbilisi State University

Professor

1995-2022

International Black Sea University

Full Professor


Work Abroad

Form of activity

Date

Place and Institution

Delivering a course of lectures at foreign higher education institutions

2009

 

2011

Algarve University (Faro, Portugal)

 

Lisbon Technical University (Portugal)

Long-term academic mission to research institutions

1965, 1979, 1990

 

 

 2002-2004

 1986, 1989, 1991, 2001, 2003

 

 

1996

 1993, 1997, 2001, 2003

1995-2005

Adam Mickiewicz Poznan University, Mathematical Institute of Polish Academy of Sciences (Poland) 

 

Algarve University (Faro, Portugal)

Mathematical Institute of Czech Academy of Sciences (Prague)

 

Radgers and Washington Universities (USA)

Sassex and Cardiff Universities (UK)

Friedrich Schiller University (Jena, Germany)   


Sphere of Scientific Interests

 

Linear and Nonlinear Harmonic Analysis, Approximation Theory, Boundary Value problems for Analytic and Harmonic Functions

 
 Textbooks, Additional Manuals, and other Methodological Literature and Training means

Years

 

2009

Calcucus I,  Lecture Notes

2009

Calcucus II, Lecture Notes

2010

Differential Equations, Lecture Notes

 
 Participation in Scientific Symposiums, Conferences for the last ten years

Years

Title

Name of Event

2004

On a progress in the theory of integral operators in weighted Banach function spaces.

Abstracts of the International Conference “Function Spaces, Differential Operators and Nonlinear Analysis” - FSDONA 2004, Svratra, Czech republic

2006

Two-weighted inequalities for classical integral operators in variable Lebesgue spaces

Workshop on Integral Operator Theory, Osaka, Japan

2006

Boundary value problems in the frame of function spaces with non-standard growth

Partial Differential Equation Conf., Tokai Univ., Japan

2007

Two-weight estimates for differential and integral operators and applications

Two-weighted Inequalities for Differential and Integral Operators, Astana, Kazachstan

2007

Harmonic analysis operators in function spaces with nonstandard growth condition

6-th ISAAC Congress, Turkey

2007

Riemann-Hilbert problem in the class Cauchy type integrals with densities from variable exponent spaces

6-th ISAAC Congress, Turkey

2008

Two weighted inequalities in variable exponent Lebesgue spaces and applications, Invited Speaker

International Conference in Function Spaces and Applications, Frayburg, Germany

2008

For Fourier Operators, Invited Speaker

International Conference in Function Spaces & Diff. Operators and Nonlinear Analysis, Helsinki, Finland

2009

Two weight Inequalities for Integral Operators, Invited Speaker

International Conference Inequalities of Analysis and Homogenization Theory, Luleo University, Sweden

2009

Methods of Nonlinear Harmonic Analysis Operators in Boundary Value Problems of Analytic and Harmonic Functions, Plenary Speaker

ISAAC Congress 7, IMPERIAL COLLEGE, London, UK

2010

Weighted Problems for Integral Operators in Some Banach Function Spaces, Plenary Speaker

International School on Nonlinear Analysis, Function Spaces and Applications, Prague, Czech Republic

2010

Three lectures on: Weighted Problems for Harmonic Analysis Operators in Some Banach Function Spaces

Summer School "Harmonic Analysis and Applications", Lisbon, Portugal

2011

Variable exponent Smirnov classes and BVP in non-standard Banach Function spaces (Plenary Speaker)

An International Conference ''Integral and Differential Operators and Their Applications'' (IDOTA), Aveiro, Portugal

2011

The Fourier operators in weighted grand Lebesgue spaces

Workshop in Harmonic Analysis and its Interaction with Operator Theory. Harmonic Analysis, Inequalities and Homogenization Theory and Applications, Sevilla, Spain

2011

The Riemann boundary value problem for analytic functions within the framework of the Grand Lebesgue Space (Plenary Speaker)

A Summer School and a Workshop '' New Function Spaces and PDE's and Harmonic Analysis'', Naples, Italy

2011

New trends in BVP of analytic and harmonic functions in the domains with non-smooth boundaries

8 th International Conference in Function Spaces, Differential Operators and Nonlinear Analysis (FSDONA 8), Germany, Tabaz/Turingia

2012

Harmonic Analysis operators and approximations problems in new function spaces

International Conference "Function Spaces X", Poznan, Poland

2012

Trace inequalities criteria in grand Lebesgue spaces

Memorial Conference in Honor of M. Krbec 

2013

Approximation of functions in nonstandard Banach function spaces

9th International ISAAC Congress, Krakow, Poland

2013

Calderón-Zygmund type singular integrals in weighted grand Lebesgue spaces and applications

IV Annual Conference of the Georgian Mathematical Union, Batumi, Georgia

 
 Organizational Work (Holding of Congresses and Conferences, Editorial Work)

Years

Name

2003

Internationa Conference Modern Aspects in Function Spaces, Differential Operators and Nonlinear Analysis, Tbilisi, Georgia

2005

International School and Workshop on Function Spaces, Integral Transforms and Applications in PDE, Tbilisi, Georgia

2008

Workshop "Variable Exponent Analysis and Related Topics", Tbilisi, Georgia

1989-2022

Chief-Editor of Proceedings of A. Razmadze Mathematical Institute

 
International and Local Scientific grants

Years

Name

1998

EPRSC (UK) No Jr. 33 034/01

2007

NATO-TUBITEK 4 181

1997-1999

Grant of Georgian Academy of Sciences N 1.7

2000-2001

Grant of Georgian Academy of Sciences  N 1.7

2002-2003

Grant of Georgian Academy of Sciences  N 1.7.02

2004-2005

Grant of Georgian Academy of Sciences  N 1.7.04

2006-2008

GNSF/ST06/3-010

2006-2008

INTAS Grant  No: 06-1000017-8792                 

2005-2008

INTAS Grant  No: 05-1000008-8157                 

2008-2010

GNSF/ST07/3-169                                               

2010-2012

GNSF/ST09_23_3-100

2012-2015

Shota Rustaveli National Science Foundation Grant  Contract N D-13/23)

2013-2016

Shota Rustaveli National Science Foundation Grant   Contract N  31/47)

 
Other Activities

Date

Name

Years

Supervision of Theses and Masters work

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Ambassador of ICM2014 (Seoul, August 13-21, 2014, Corea)

 

1. Potential type integrals and maximal functions in weighted spaces

 

2. Fractional maximal functions and potentials in weighted spaces

 

3. Generalized maximal functions in fractional integrals

 

4. Metric and approximate properties of Fourier series in weighted function spaces

 

5. Two-weighted problems for discrete operators

 

6. Two-weight inequalities for singular integrals defined on homogeneous groups

 

7. Boundedness and compactness criteria for potential type operators

 

8. Some problems of Fourier analysis and ergodic theory

 

9. Fourier multipliers and maximal functions

 

10. Fourier operators in Lebesgue spaces with nonstandard weights

 

1986

  

1988

 

1990

  

1996

 

 

1998

 

1998

 

 

2001

 

2003

 

2005

 

2005

 

2014


Awards and Prizes, Honorary Title

Date

Name of Awards, Prizes, Honorary Title

1985

Andrea Razmadze Prize of Georgian National Academy of Sciences

 
 

Publications

(i) monographs:

  1. V. Kokilashvili, Maximal functions and singular integrals in weighted function spaces. (Russian) Metsniereba, Tbilisi, 1985, pp. 114.

  2. V. Kokilashvili and M. Krbec, Weighted inequalities in Lorentz and Orlicz spaces. World Scientific, 1991.

  3. I. Genebashvili, A. Gogatishvili, V. Kokilashvili, and M. Krbec, Weight Theory for Integral Transforms on Spaces of Homogeneous Type. Pitman Monographs and Surveys in Pure and Applied Mathematics. Addision Wesley Longman 1998, 234 pages.

  4. G. Khuskivadze, V. Kokilashvili and V. Paatashvili, Boundary Value Problems for Analytic and Harmonic Functions in Domains width Non-Smooth Boundaries. Applications to Conformal Mappings. Mem. Differential Equations Math. Phys.  14 (1998), 1-195.

  5. D. E. Edmunds, V. Kokilashvili, and A. Meskhi, Bounded and compact integral operators. Mathematics and its Applications, 543. Kluwer Academic Publishers, Dordrecht, 2002. 

  6. V. Kokilashvili, A. Meskhi  and L. E. Persson, Weighted Norm Inequalities for Integral Transforms with Product Kernels. Nova Science Publishers, New-York, USA, 2009.

  7. V. Kokilashvili and V. Paatashvili, Boundary Value Problems for Analytic and Harmonic Functions  in Nonstandard Banach Function Spaces. Nova Science Publishers, New-York, USA, 2012.

  8. V. Kokilashvili, A. Meskhi, S. Samko, and H. Rafeiro, Integral operators in non-standard function spaces. Vol. I. Variable exponent Lebesgue and Amalgam spaces. Birkhhäuser, 2016, pp. 1-576.

  9. V. Kokilashvili, A. Meskhi, S. Samko, and H. Rafeiro, Integral operators in non-standard function spaces. Vol. II. Variable exponent Hölder, Morrey-Campanato and Grand spaces. Birkhhäuser, 2016, pp. 577-1005.

     

 

(ii) papers:

  1. Some remarks concerning Fourier coefficients and function classes. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 28 (1962), No. 1, 3-8.

  2. On best approximation of functions and Fourier-Lebesgue coefficients. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 30 (1963), No. 3, 265-275.

  3. On generalized lacunary Fourier series. (Georgian) Soobshch. Akad. Nauk Gruzin. SSR 31 (1963), No. 2, 257-262.

  4. On converse theorem of constructive theory of functions in Lp spaces. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 29 (1964), 183-189.

  5. On some function space and Fourier coefficients. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 35 (1964), No. 3, 523-530.

  6. On estimate of best approximations and modulus of smoothness in Lebesgue spaces of periodic functions with transformed Fourier series. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 35 (1964), No. 1, 3-8.

  7. Best approximations by trigonometric polynomials in Orlicz spaces and Fourier-Lebesgue coefficients. Bull. Acad. Polon. Sci., Ser. Math. 13 (1965), No. 5, 357-362.

  8. Best approximation of functions by Walsh polynomials and Walsh-Fourier coefficients. Bull. Acad. Polon. Sci., Ser. Math. 13 (1965), No. 6, 405-410.

  9. On some properties of conjugate functions of two variables. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 40 (1965), No. 2, 263-270.

  10. On relation between Fourier-Lebesgue coefficients and modulus of continuity of functions of two variables. (Russian) Trudy Tbiliss. Univ. 110 (1965), 247-254.

  11. The converse theorem of constructive theory of functions in Orlicz spaces. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 37 (1965), No. 2, 263-270.

  12. On approximation of periodic functions by certain linear operators. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 43 (1966), No. 2, 257-260.

  13. On approximation of functions. (Russian) Abstracts of International Congress of Math., Section 4, Moscow, (1966), 57.

  14. On structure and constructive characteristics of certain class of periodic functions. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 43 (1966), No. 1, 3-8.

  15. On proximate order of best approximations of analytic functions by generalized-lacunary series with respect to Faber polynomials. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 41 (1966), No. 3, 529-534.

  16. On approximation of periodic functions in Orlicz spaces. Bull. Acad. Polon. Sci., Ser. Math. 14 (1966), 2, 305-310.

  17. On mean approximation of analytic functions from Ep classes. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 47 (1967), No. 1, 3-6.

  18. *On mean approximation of analytic functions from Ep classes. (Russian) Dokl. Akad. Nauk SSSR 117 (1967), No. 2, 261-264.

  19. On approximation by Walsh-Fourier means. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 45 (1967), No. 2, 305-310.

  20. On summability of Fourier series by ultraspherical polynomials and best approximations. (Russian) Soobshch. Akad. Nauk Gruzin. SSR  58 (1967), No. 1, 3-6.

  21. *On analytic functions of Smirnov-Orlicz classes. Studia Math. 31 (1968), 152-174.

  22. On approximation of periodic functions. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 34( 1968), 51-81.

  23. On approximation of analytic functions from Ep classes. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 34 (1968), 82-102.

  24. *The direct theorem on mean approximations of analytic functions. (Russian) Dokl. Akad. Nauk SSSR 185 (1969), 749-752.

  25. On multipliers and decomposition of series by polynomial solutions of elliptic type differential equations. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 56 (1969), No. 1, 25-28.

  26. On mean approximation of regular solutions of elliptic type differential equations. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 56 (1969), No. 3, 529-532.

  27. On boundedness of singular integral operators in Lp spaces with weight. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 64 (1971), No. 1, 17-20.

  28. On boundedness of singular integral operators in weighted spaces. (Russian) In: Proc. of Symposium on Continuum Mechanics and Related Problems of Analysis (Tbilisi, 23-29. IX. 1971), vol. 1, Metsniereba, Tbilisi, 1973, 125-141.

  29. On conjugate functions. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 68 (1972), No. 3, 537-540.

  30. On coefficients of power series and Fourier series. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 42 (1972), 78-86.

  31. On multipliers and decomposition of trigonometric Fourier series. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 43 (1973), 87-110.

  32. On boundary properties of functions of certain classes. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 43 (1973), 72-86.

  33. On boundedness of singular operators with Cauchy kernels in weighted spaces. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 77 (1975), No. 3, 529-532.

  34. On boundedness of some translation invariant operators. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR, 47 (1975), 14-33.

  35. *On multipliers of Fourier transforms. (Russian) Dokl. Akad. Nauk SSSR 220 (1975), No. 1, 19-22.

  36. *On singular integrals and maximal operators with Cauchy kernel. (Russian) Dokl. Akad. Nauk SSSR 223 (1975), No. 3, 555-558.

  37. *On boundary problem of linear conjugation with measurable coefficients. (Russian) Dokl. Akad. Nauk SSSR 224 (1975), No. 5, 1008-1011(with V. Paatashvili).

  38. *On multipliers of Fourier transforms and imbedding theorems in some function spaces. (Russian) Mat. Zametki 20 (1976), No. 4, 605-610.

  39. On singular integrals and multipliers of Fourier transforms. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 53 (1976), 38-61.

  40. On boundary value problems of linear conjugation with measurable coefficients. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 55 (1977), 59-22 (with V. Paatashvili).

  41. On maximal singular integral operator with Cauchy kernel. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 55 (1977), 38-58.

  42. *Maximal inequalities and multipliers in weighted Lizorkin-Triebel spaces. (Russian) Dokl. Akad. Nauk SSSR 239 (1978), No. 1, 42-45 (English transl.: Soviet Math. Dokl. 19 (1978), 272-276).

  43. On traces of functions with partial derivatives from Orlicz classes. Comment. Math. Tomus spec. in hon. Ladislai Orlicz PWN, Polish Akad. Sci., Warcaw, 1978, 183-189.

  44. On weighted inequalities for singular integrals with Cauchy kernel on smooth contours. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 90 (1978), No. 3, 537-540.

  45. Boundary value problems with measurable coefficients for one class of boundary curves. (Russian) Soobshch. Akad. Nauk Gruzin. SSR  91 (1978), No. 1, 25-27 (with V. Paatashvili).

  46. Bessel anisotropic potentials and imbedding theorems for limiting index. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 58 (1978), 134-149.

  47. On Calderon type singular integrals. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 61 (1979), 5-14.

  48. On some integral operators in weighted spaces. (Russian) In: Shkoli po teorii oper. v funct. prostr. Izd. Novosibirs. univ., Novosibirsk, 1979, 1-20.

  49. On Hardy inequalities. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 96 (1979), No. 1, 39-40.

  50. Maximal functions in weighted spaces. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 65 (1980), 110-121.

  51. Weighted inequalities for maximal functions with respect to Vitali regular family. (Russian) Soobshch. Akad. Nauk Gruzin. SSR  98 (1980), No. 3, 545-547.

  52. Weighted inequalities for maximal functions with respect to Vitali regular family. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin.SSR 66 (1980), 36-45.

  53. On multiple Hilbert transforms and multipliers in weighted spaces. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 98 (1980), No. 2, 285-288.

  54. *Discontinuous problem of linear conjugation and singular integral equations. (Russian) Differentsial'nye Uravneniya 16 (1980), No. 9, 1650-1659 (with V. Paatashvili). (English transl.: Diff. Equat. 16 (1980), No. 9, 1067-1075).

  55. Bisingular integral operators in weighted spaces. (Russian) Soobshch. Akad. Nauk Gruzin. SSR 101 (1981), No. 2, 289-282.

  56. Singular integral operators in weighted spaces. In: Colloquia Math. Soc. J. Boyai 35, Functions, Series, Operators. Budapesht, 1980, 707-714.

  57. On weighted Lizorkin-Triebel spaces. Singular integrals, multipliers, imbedding theorems. (Russian) Trudy Mat. Inst. Steklov. 161 (1983), 125-149. (English transl.: Proc. Steklov Inst. Mat. 3 (1984), 135-162.)

  58. On singular and bisingular integral operators in weighted spaces. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 69 (1982), 51-79.

  59. On traces for weighted anisotropic Lizorkin-Triebel spaces. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 73 (1983), 88-98.

  60. Anisotropic maximal inequalities with weights. In: Proc. Conf. Constr. Theory of functions'84, Sofia, 1984, 473-478 (with J. Rakosnik).

  61. On the boundedness of Riesz potentials and fractional maximal functions. In: Proc. Conf. Constr. Theory of functions'84, Sofia, 1984, 470-472.

  62. *Weighted inequalities for Riesz potentials and fractional maximal functions in Orlicz spaces. Soviet Math. Dokl. 32 (1985), No. 1, 70-73 (with M. Krbec).

  63. Weighted norm inequalities for anisotropic maximal functions. Casopis pro pest. math. 110 (1985), 384-393.

  64. *Weighted norm inequalities for vector-valued anisotropic maximal functions. Zeitshrift für Analysis und ihre Anwendungen, Bd. 4 (1985), No. 6, 503-511 (with J. Rakosnik).

  65. *Weighted inequalities for anisotropic potentials and maximal functions. (Russian) Dokl. Akad. Nauk SSSR 282 (1985), No. 6, 1304-1306 (English transl.: Soviet Math. Dokl. 31 (1985), No. 1, 583-585) (with M. Gabidzashvili).

  66. Weighted inequalities for some integrals transforms. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 76 (1985), 100-106.

  67. Maximal functions and potential type integrals in weighted Lebesque and Lorentz spaces. (Russian) Trudy Mat. Inst. Steklov 172 (1985), 192-201. (English transl.: Proc. Steklov Inst. Mat. 172( 1987), No. 3).

  68. On boundedness of anisotropic fractional maximal functions and potentials in weighted Orlicz spaces. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 82 (1986), 106-115.

  69. *Weighted inequalities for maximal functions and fractional integral in Lorentz spaces. Math. Nachr. 133 (1987), 33-42.

  70. Anisotropic maximal functions and potentials in weighted Lorentz spaces. (Russian) Trudy Math. Inst. Steklov 180 (1987), 136-138; English transl.: Proc. Steklov Inst. Mat. 3 (1989) , 159-161.

  71. Weighted estimates for maximal functions and fractional integrals in Lorentz spaces. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzin. SSR 86 (1987), 74-85. (English transl. in: Integral Operators and Boundary Properties of functions. Fourier Series. Nova Science Publishers. Inc., 101-117).

  72. Singular integral in weighted Orlicz classes. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 89 (1988), 42-50.

  73. Singular integral in weighted Orlicz classes. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk. Gruzin. SSR 89 (1988), 42-50.

  74. Fractional integrals on spaces of homogeneous type. Comment. Math. Univ. Carolinae 30 (1989), No. 3, 511-523 (with A. Kufner).

  75. Fractional integrals on curves. Trudy Tbiliss. Mat. Inst. Razmadze 95 (1989), 56-70.

  76. *Potentials on thin sets. (Russian) Dokl. Akad. Nauk SSSR 301 (1989), No. 5, English transl.: Soviet Math. Dokl. 40 (1990), No. 2, 400-402.

  77. Weighted estimates for classical integral operators. In: Proceedings of the International Spring Scool: ``Nonlinear Analysis, Function Spaces and Applications IV'', Roudnice nad Labem Czechoslovakia, 1990, May 21-25, Tcubner-Texte zur Mathematik, Teubner Verlag, Leipzig , 1990, 86-103.

  78. On a weight problem for integrals with positive kernels. Bull. Georg. Acad. Sci. 140 (1990), No. 3, 145-148.

  79. *Weighted estimates for fractional integrals on curves. (Russian) Dokl. Akad. Nauk SSSR 310 (1990), No. 1, 14-17; English transl.: Soviet Math. Dokl. 41 (1990), 5-7 (with M. Gabidzashvili).

  80. On a weight problem for integrals with positive kernels. Bull. Georgian Acad. Sci. 140 (1990), No. 3, 145-148.

  81. A two weight weak type inequality for potential type operators. Comment. Math. Univ. Carolinae 32 (1991), No. 2, 251-263 (with J. Rakosnik).

  82. Potentials on thin sets. (Russian) In: ``Function Spaces and Appl. Diff. Equat.'' Izd. Univ. Druzbi Narodov, Moskva, 1992, 25-47.

  83. Two-weight inequalities for generalized potentials. Trudy Mat. Inst. Steklov 194 (1992), 89-96; English transl.: Proc. Steklov Inst. Mat. 1993, No. 4, 91-99 (with M. Gabidzashvili, I. Genebashvili).

  84. Potentials on thin sets. (Russian) In: ``Function Spaces and Appl. Diff. Equat.'' Izd. Univ. Druzbi Narodov, Moskva, 1992, 25-47.

  85. Solution of some weight problems. In: ``Function Spaces, Differential Operators and Nonlinear Analysis''. Teubner-Texte zur Mathematik 133 , 264-273, Teubner-Verlag, Leipzig, 1993.

  86. Riesz potential in weighted Lorentz spaces. In: Continuum Mechanics and Related Problems of Analysis. Proc. Int. Symp. Metsniereba Publishing House, Tbilisi , 1993, 382-389.

  87. Weighted norm inequalities for fractional maximal functions and integrals defined on homogeneous type spaces. Proc. A. Razmadze Math. Inst. 106(1993), 63-76 (with J. Genebashvili).

  88. *Two-weight estimates for multipliers, and imbedding theorems. (Russian) Dokl. Akad. Nauk 336 (1994), No. 4, 439-441; English transl.: Russian Acad. Sci. Dokl. Math. 49 (1994), No. 3, 515-519 (with P. I. Lizorkin).

  89. *Two-weighted estimates for some integral transforms in Lebesgue spaces with maxed norm and imbedding theorems. Georgian Math. J. 1 (1994), No. 5, 495-503.

  90. *Two-weight inequalities for singular integrals. Canad. Bull. Math. 38 (1995), No. 3, 295-303 (with D. E. Edmunds).

  91. New aspects in weight theory. In: Function Spaces, Differential Operators and Nonlinear Analysis. Prometeus Publishing House, Prague, 1996, 51-70.

  92. *Weighted inequalities for Hilbert transforms and multiplicators of Fourier series. J. Inequalities and Applications 1 (1997), No. 3, 239-252 (with A. Meskhi).

  93. Two-weight inequalities for singular integrals defined on homogeneous groups. Proc. Razmadze Math. Inst. 112 (1997), 57-90 (with A. Meskhi).

  94. *Two-weight inequalities for singular integrals on homogeneous groups. (Russian) Dokl. Akad. Nauk 354 (1997), No. 3, 301-303 (with A. Meskhi).

  95. *On the Riemann-Hilbert problem in the domain with non-smooth boundary. Georgian Math. J. 4 (1997), No. 3, 279-302 (with V. Paatashvili).

  96. Two-weighted inequalities for Hardy type operator on Lorentz spaces defined on homogeneous groups. Proc. A. Razmadze Math. Inst.  112 (1997), 138-140 (with and A. Meskhi).

  97. Two-weighted inequalities for singular integrals on Lorentz spaces defined on homogeneous groups. Proc. A. Razmadze Math. Inst.  112 (1997), 143-145 (with A. Meskhi).

  98. Two-weighted inequalities for singular integrals on homogeneous type spaces. Proc. A. Razmadze Math. Inst.  114 (1997), 119-123 (with A. Meskhi).

  99. Neumann problem in the class of harmonic functions in domain with a piecewise-Lyapunov boundary. Mem. Differential Equations Math. Phys. 12 (1997) (with V. Paatashvili).

  100. Boundedness and compactness of Hardy-type operators on Banach function spaces defined on measure spaces. Proc. A. Razmadze Math. Inst.117 (1998), 7-30 (with D. Edmunds and A. Meskhi).

  101. Two-weight compactness criteria for potential type operators. Proc. A. Razmadze Math. Inst. 117(1998), 123-125 (with D. Edmunds).

  102. On compactness for potentials on SHT. Proc. A. Razmadze Math. Inst. 121 (1999), 153-154.

  103. On the compactness of weak singular integral operators on regular curves. Bull. Georgian Acad. Sci. 161 (1999).

  104. *Two-weighted inequalities for integral operators in Lorentz spaces on homogeneous groups. Georgian Math. J. 6 (1999), No. 1, 65-85 (with A. Meskhi).

  105. Riemann-Hilbert problem in the domain with piecewise smooth boundaries. Bull. Georgian Acad. Sci. 159 (1999), No. 1, 11-14 (with V. Paatashvili).

  106. On the Dirichlet and Neumann problem in the domains with piecewise smooth boundaries. Bull Georgian Acad. Sci. 159 (1999), No. 2, 181-184 (with V. Paatashvili).

  107. *Two-weight estimates for singular integrals defined on homogeneous type spaces. Canadian J.  Math. 52 (2000), No. 3, 468-502 (with D. Edmunds and A. Meskhi).

  108. Boundedness and compactness criteria for some classical integral transforms. Function spaces (Poznań, 1998), 279-296, Lecture Notes in Pure and Appl. Math., 213, Dekker, New York, 2000 (with A. Meskhi).

  109. On the boundedness and compactness of generalized truncated potentials. Bull. TICMI 4 (2000), 28-31 (with A. Meskhi).

  110. Norms of positive operators on some cones of functions defined on measure spaces. Proc. A. Razmadze Math. Inst. 122 (2000), 59-78 (with A. Meskhi).

  111. *Weight inequalities for the integrals defined on homogeneous and nonhomogeneous type spaces. Georgian Math. J. 8 (2001), No. 1, 33-59 (with D. Edmunds and A. Meskhi).

  112. A survey of recent results of Georgian mathematicians on boundary value problems for holomorphic functions. Mem. Differential Equations Math. Phys.23 (2001), 85-138.

  113. *On a trace inequality for one-sided potentials and applications to the solvability of nonlinear integral equations. Georgian Math. J. 8 (2001), No. 3, 521-536 (with A. Meskhi).

  114. *Boundedness and compactness criteria for the generalized truncated potentials. (Russian) Trudy Mat. Inst. Steklov. 232 (2001), 164-178; Engl. Transl.Proc. Steklov Inst. Math. 232 (2001), 157-171 (with A. Meskhi).

  115. *Fractional integrals on measure spaces Fract. Calc. Appl. Anal. 4 (2001), No. 1, 1-24 (with A. Meskhi).

  116. Criteria for the boundedness and compactness of operators with power-logarithmic kernels. Anal. Math. 27 (2001), No. 2, 173-185 (with A. Meskhi).

  117. Weight problems for higher dimensional singular integrals via Clifford analysis. Proc. of the NATO ARW, Prague, October 30-November 3, 2000, 247-253, F. Brackx, J. S. R. Chisholm, and V. Soucek (eds.), Kluwer Academic Publishers, Dordrecht, 2001 (with A. Meskhi).

  118. *On Fourier multipliers in weighted Triebel-Lizorkin spaces. J. Inequal. Appl. 7 (2002), No. 4, 555-591 (with D. Edmunds and A. Meskhi).

  119. Weight inequalities for one-sided potentials for critical weights. Fract. Calc. Appl. Anal. 25 (2002), 255-265 (with A. Meskhi). 

  120. *A problem of linear conjugation for analytic functions with boundary values from the Zygmund class. Georgian Math. J. 9 (2002), 309-324 (with V. Paatashvili). 

  121. Maximal and fractional operators in weighted L p(x) spaces. Proc. A. Razmadze Math. Inst. 129 (2002), 145-149 (with S. Samko). 

  122. Singular integrals and potentials in some Banach function spaces with variable exponent. Proc. A. Razmadze Math. Inst. 129 (2002), 150-155 (with S. Samko). 

  123. *Singular integrals in weighted Lebesgue spaces with variable exponent. Georgian Math. J. 10 (2003), No. 1, 145-156 (with S. Samko).

  124. Singular integral equations in the Lebesgue spaces with variable exponent. Proc. A. Razmadze Math. Inst. 131 (2003), 61-78 (with S. Samko).

  125. Two-weighted estimates for Fourier multipliers in Lebesgue spaces. Proc. A. Razmadze Math. Inst. 132 (2003), 148-149.

  126. On the inversion and characterization of the Riesz potentials in the weighted Lebesgue spaces. Mem. Differential Equations Math. Phys. 29 (2003), 31-45 (with A. Meskhi and S. Samko).

  127. *On Sobolev theorem for Riesz-type potentials in Lebesgue spaces with variable exponent. Z. Anal. Anwendungen 22 (2003), No. 4, 1-12 (with S. Samko).

  128. *Singular integrals and potentials in some Banach function spaces with variable exponent. J. Funct. Spaces Appl. 1 (2003), No. 1, 45-59 (with S. Samko).

  129. *The Dirichlet problem for harmonic functions with boundary values from Zygmund classes. Georgian Math. J. 10 (2003), No. 3, 531-542 (with V. Paatashvili).

  130. Boundary value problems for analytic and harmonic functions of Smirnov classes in the domains with nonsmooth boundaries. Proc. Conf. in Madeira in honour of Prof. G. Litvinchuk, Kluwer Academic Publishers, 2003 (with V. Paatashvili and Z. Meshveliani).

  131. On Fourier multipliers. J. Anal. Appl. 1 (2003), No. 3, 143-155 (with D. E. Edmunds).

  132. *On a trace inequality for one-sided potentials with multiple kernels. Fract. Calc. Appl. Anal. 6 (2003), No. 4, 461-472 (with A. Meskhi).

  133. *A trace inequality of generalized potentials in Lebesgue spaces with variable exponent. J. Funct. Spaces Appl. 2 (2004), No. 1, 55-69 (with D. E. Edmunds and A. Meskhi).

  134. *Maximal and fractional operators in weighted L p(x) spaces. Revista Math. Iberoamericana 20 (2004), No. 2, 493-515 (with S. Samko).

  135. On the solvability of divergence equation in the theory of incompressible fluids. Mem. Differential equations Math. Phys. 31 (2004), 131-134.

  136. Sobolev theorem for potentials on Carleson curves in variable Lebesgue spaces. Mem. Differential equations Math. Phys. 33 (2004), 157-158 (with S. Samko).

  137. *On the boundedness and compactness of weight Hardy operators in L p(x) spaces. Georgian Math. J. 12 (2005), No. 1, 27-44 (with D. E. Edmunds and A. Meskhi).

  138. On a progress in the theory of integral operators in weighted Banach Function Spaces. In: "Function Spaces, Differential Operators and Nonlinear Analysis", Proc. Conf. in honour of A. Kufner, Svrtka, May 27 - June 1, 2004; Math. Inst. Acad. Sci. of Czech Republic, Praha, 2005, 152-175.

  139. *Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in L p(·)(G). Bound. Value Probl. 2005, No. 1, 43-71 (with V. Paatashvili and S. Samko ).

  140. *On some two-weighted inequalities for fractional integrals on homogeneous spaces. Z. Anal. Anwendungen 24 (2005), No. 4, 871-885 (with A. Meskhi).

  141. On two-weight estimates for strong fractional maximal functions and potentials with multiple kernels. Proc. A. Razmadze Math. Inst. 137 (2005), 135-140 (with A. Meskhi).

  142. Weighted boundedness in Lebesgue spaces with variable exponents of classical operators on Carleson curves. Proc. A. Razmadze Math. Inst. 138 (2005), 106-110 (with S. Samko).

  143. Strong and iterated maximal functions and applications to the mean summability of the double trigonometric Fourier series. Proc. A. Razmadze Math. Inst. 139 (2005), 128-132 (with A. Meskhi and Ts. Tsanava).

  144. *On one-sided potentials with multiple kernel. Integral Transforms and Special Functions 16 (2005), No. 8, 669-683 (with A. Meskhi).

  145. Boundedness in Lebesgue spaces with variable exponent of maximal, singular and potential operators. Izv. Visshikh Uchebn. Zaved. Severo-Kavk. Region, 152-157 (2005) (with S. Samko).

  146. * The maximal operator in variable spaces $L^{p(\cdot)}(\Omega,p)$ with oscillating weight. Georgian Math. J. 13 (2006), No. 1, 109-125 (with N. Samko and S. Samko).

  147.   Two-weighted criteria for integral transforms with multiple kernels. Banach Center Publ. 72 (2006), 119-140 (with A. Meskhi).

  148. *On the mean summability by Cesaro method of Fourier trigonometric series in two-weighted setting. J. Inequal. Appl. 2006, Art. ID 41837, 15 pp. (with A. Guven).

  149. Boundedness in Lebesgue spaces with variables exponent of the Cauchy integral operator on Carleson curves. Operator Theory: Advances and Applications, devoted to the 70th birthday of Prof. I.B. Simonenko 170 (2006), 167-186 (with V. Paatashvili and S. Samko).

  150. *Singular operators in $L^{p(\cdot)}(\omega,\rho)$ with oscillation weights. Math. Nachr. 280 (2007), No. 9-10, 1-12 (with N. Samko and S. Samko).

  151. *The Dirichlet problem for harmonic functions in the Smirnov class with variable exponent. Georgian Math. J. 14 (2007), No. 2, 289-299 (with V. Paatashvili).

  152. On a generalization of Calderon-Zygmund theorem in weighted Lebesgue spaces with variable exponent. Bull. Georgian National Acad. Sci. 175 (2007), No. 1, 34-39 (with S. Samko).

  153. Approximation in weighted Lebesgue and Smirnov spaces with variable exponents. Proc. A. Razmadze Math. Inst. 143 (2007), 25-35 (with D. Israfilov and S. Samko).

  154. On the approximation in weighted Lebesgue spaces. Proc. A. Razmadze Math. Inst. 143 (2007), 103-113 (with Y. E. Yildirir).

  155. Two-weight estimates for Fourier operators and Bernstein inequality. Proc. A. Razmadze Math. Inst. 143 (2007), 127-130 (with A. Guven).

  156. On the means of Fourier integrals and Bernstein inequality in two-weighted setting. Proc. A. Razmadze Math. Inst. 143 (2007), 131-134 (with A. Guven).

  157. On one-sided operators in variable exponent Lebesgue spaces. Proc. A. Razmadze Math. Inst. 144 (2007), 126-131 (with D. E. Edmunds and A. Meskhi).

  158. The maximal operator in weighted variable spaces on metric measure spaces. Proc. A. Razmadze Math. Inst. 144 (2007), 137-144 (with S. Samko).

  159. The Riemann-Hilbert problem in domains with piecewise-smooth boundaries in classes of Cauchy type integrals with density from $L\sp {p(·)}(\Gamma)$. Proc. A. Razmadze Math. Inst. 145 (2007), 103-108 (with V. Paatashvili).

  160. A general approach to weighted boundedness of operators of harmonic analysis in variable exponent Lebesgue spaces. Proc. A. Razmadze Math. Inst. 145 (2007), 109-116 (with S. Samko).

  161. *Weighted criteria for generalized fractional maximal functions and potentials in Lebesgue spaces with variable exponent. Integral Transforms Spec. Funct. 18 (2007), No. 9-10, 609-628 (with A. Meskhi).

  162. *Two-weight estimates for singular and strongly singular integral operators. Acta Math. Hungar. 116 (2007), No. 1-2, 1-25 (with N. Lyall and A. Meskhi).

  163. *The maximal operator in weighted variables spaces $L^{p(\cdot)}$. J. Funct. Spaces Appl. 5 (2007), No. 3, 299-317 (with N. Samko and S. Samko).

  164. Two-weight estimates for strong maximal functions, potentials and singular integrals with multiple kernels. Evraz. Mat. Zh., 2007, No. 2, 31-46 (with A. Meskhi).

  165. *Boundedness of maximal and potential on Carleson curves in Lebesgue spaces with variable exponent. Acta Math. Sinica English series, 2008, DoI: 10.1007/s10114-008-6464-1 (with S. Samko).

  166. *One-sided operators in Lp(x) spaces. Math. Nachr. 281 (2008), No. 11, 1525-1548 (with D. E. Edmunds and A. Meskhi).

  167. *Operators of Harmonis Analysis in weighted spaces with non-standard growth. J. Math. Anal. Appl.  (2008); doi:10, 1016/j.jmaa 2008.06.056 (with S. Samko).

  168. *The maximal operator in weighted variable exponent spaces in metric spaces. Georgian Math. J. 15 (2008), No. 4, 683-712 (with S. Samko).

  169. Fractional, maximal and singular integral operators in variable Lorentz spaces. Fract. Calculus and Appl. 11 (2008), No. 4, 407-420 (with L. Ephremidze and S. Samko).

  170. On the maximal and Fourier operators in weighted Lebesgue spaces with variable exponent, Proc. A. Razmadze Math. Inst. 146 (2008), 120-123 (with A. Meskhi).

  171. Vekua's generalized singular integrals on Carleson curves in weighted Lebesgue spaces. Operator Theory: Advances and Applications 181 (2008), 283-293 (with S. Samko).

  172. Weighted boundedness of maximal singular and potential operators in variable exponent spaces. In A. A. Kilbas and S. V. Rogozin, editors, Analytic methods of Analysis and Differential Equations, pages 139-164. Cambridge Scientific Publishers, 2008 (with S. Samko).

  173. *The Riemann-Hilbert problem in weighted classes of Cauchy-type integrals with density from $L^{p(\cdot)}(\Gamma)$. Complex Anal. and Operator Theory. 2 (2008), No. 4, 569-591 (with V. Paatashvili).

  174. Singular operators and Fourier multipliers in weighted Lebesgue spaces with variable exponent. (Russian) Vestnik St. Petersburg Univ. Mathematics 41 (2008), No. 2, 134-144 (with S. Samko).

  175. *Riemann problem in the class of Cauchy-type integrals with density in . Doklady Mathematics, 78 (2008), No. 1, 510-513 (with V. Paatashvili and S. Samko).

  176. Boundedness of maximal and singular operators in Morrey spaces with variable exponent. Armenian J. Math. 1 (2008), No. 1, 18-28 (with A. Meskhi).

  177. On variable Hardy and Smirnov classes of analytic functions. Georgian International Journal of Sciences. Nova Science Publishers, Inc. 1 (2008),  No. 2, 67-81 (with V. Paatashvili).

  178. *Two-weight estimates for strong fractional maximal functions and potentials with multiple kernels. J. Korean Math. Soc. 46 (2009), No. 3, 523-550 (with A. Meskhi).

  179. *A note on the boundedness of the Hilbert transform in weighted grand Lebesgue spaces, Georgian  Math.J. 16 (2009), No. 3, 547-551 (with A. Meskhi).

  180. On the Riemann-Hilbert-Poincaré problem and I. Vekua’s representation of holomorphic functions. Bull. of the Georgian National Academy of Sci. 3 (2009), No. 1, 25-29 (with V. Paatashvili).

  181. Maximal and potential operators in variable Morrey spaces defined on non-homogeneous spaces. Bull. of the Georgian National Academy of Sci. 2 (2008), No. 3, 18-21 (with A. Meskhi).

  182. On the Calderon singular integrals in weighted variable Lebesgue spaces. Bull. of the Georgian National Academy of Sci. 2 (2008), No. 4, 3-5.

  183. *On the approximation by trigonometric polynomials in weighted Lorentz spaces, Function Spaces & Appl. 8(2010), No. 1 (with Y. Ildirir).

  184. *The Riemann-Hilbert problem in domains with piecewise-smooth boundaries in classes of Cauchy type integrals with density from . Georgian Math. J. 16 (2009), No. 4 (with V. Paatashvili).

  185. One and two weight norm estimates for one-sided operators in $L^{p(\cdot)}$ spaces. Proc. A. Razmadze Math. Inst. 148 (2008), 126-133 (with A. Meskhi and M. Sarwar).

  186. *Boundedness criteria for maximal functions and potentials on the half-space in weighted Lebesgue spaces with variable exponent. Integral Transf. Spec. Funct. 20 (2009), No. 11, 805-819  (with M. Asif and A. Meskhi).

  187. *Two-weight estimates for Fourier operators and Bernstein inequality. Studia Sci. Math. Hung. DOI: 10.1556/SScMath.2009.1109 (with A. Guven).

  188. *Two-weight estimates in $L^{p(\cdot)}$ spaces with applications to Fourier series. Houston J. Math. 35 (2009),  No. 2, 665-689 (with D. E. Edmunds and A. Meskhi).

  189. *Morrey spaces and fractional integral operators. Expositiones Mathematicae 27 (2009), 227-239 (with Eridani and A. Meskhi).

  190. A Refined Inverse Inequality of Approximation in Weighted Variable Exponent Lebesgue Spaces, Proc. A. Razmadze Math. Inst. 151 (2009), 134-138 (with S. Samko).

  191. A note on extrapolation and modular inequalities. Proc. A. Razmadze Math. Inst. 150(2009), 91-97.

  192. *Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure. Complex Variables and Elliptic Equations 55 (2010), No. 8, 923-936 (with A. Meskhi)

  193. *On the mean of Fourier integrals and Bernstein inequality in two-weighted settings. Positivity (2010) 14:165–180  (with A. Guven).

  194. Boundedness criterion for the Cauchy singular integral operator and maximal functions in weighted grand Lebesgue spaces. Bull. Georgian Nat. Acad. Sci. 3 (2009), No. 3, 5-7.

  195. *Weight characterization of the trace inequality for the generalized Riemann-Liouville transform in $L^{p(x)}$ spaces. Math. Inequalities & Appl. 13 (2010), No.1, 63-81 (with U. Ashraf and A. Meskhi).

  196. The Riemann boundary value problem analytic functions in the frame of grand  spaces. Bull. Georgian Nat. Academy of Sci. 4 (2010), No.1, 5-8.

  197. Boundedness criteria for singular integrals in weighted grand Lebesgue spaces, Journal of Math. Anal. (Springer, New-York), 170 (2010), No. 1, 20-33.

  198. Approximation by linear summability means in weighted variable exponent Lebesgue spaces, Proc. A. Razmadze Math. Inst. 154 (2010), 147-150. (with Ts. Tsanava).

  199. On the norm estimate of deviation by linear summability means and an extension of the Bernstein inequality, Proc. A. Razmadze Math. Inst. 154 (2010), 144-146. (with Ts. Tsanava).

  200. *Potential operators in variable exponent Lebesgue spaces. Two-weight estimates. J. Ineq. & Appl. Volume 2010, Article ID 329571, 27 pp., DOI:10.1155/2010/ (with A. Meskhi and M. Sarwar).

  201. On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces. Banach J. Math. Analysis 5 (2011), No. 1, 70-82 (with R. Akgűn).

  202. The Dirichlet problem for harmonic functions from variable exponent Smirnov classes in domains with piecewise-smooth boundaries. J. Math. Sci. (Springer, New-York), 172(2011), n 3, 1-21 (with V. Paatashvili).

  203. Two-weight inequalities for fractional maximal functions and singular integrals in $L^{p(\cdot)}$ spaces. J. Math. Sci. (Springer, New-York), 173 (2011), No. 6, 1-18 (with A. Meskhi).

  204. *The refined direct and converse inequalities of trigonometric approximation in weighted variable exponent Lebesgue spaces. Georgian Math. J. 18 (2011), No. 3, 399-423  (with R. Akgűn).

  205. *Weighted Hardy and Smirnov classes and the Dirichlet problem for a ring within the framework of variable exponent analysis. Complex Variables and Elliptic Equations 56 (2011), No. 10-11, 955-973 (with V. Paatashvili).

  206. *Generalization of I. Vekua’s integral representations of holomorphic functions and their application to the Riemann-Hilbert-Poincaré problem. Function Spaces and Applications 9 (2011), No. 3, 217-244 (with V. Paatashvili).

  207. *Boundedness of weighted singular integrals in grand Lebesgue spaces. Georgian Math. J.  18 (2011), No. 2, 259-269 (with S. Samko).

  208. Boundary value problems of analytic and harmonic functions in a domain with piecewise-smooth boundary in the frame of variable exponent Lebesgue spaces. Operator Theory: Advances and Appications, 216(2011), 17-39.

  209. Boundedness of weighted singular integral operators on a Carleson curves in Grand Lebesgue spaces. In ICNAAM 2010; Intern. Conf. Numer. Anal. Appl. Math., vol. 1281, pp. 490-493. AIP Confer. Proc., 2010.

  210. The Dirichlet problem for variable exponent Smirnov class harmonic functions in doubly-connected domains. Mem. Differential Equations Math. Phys. 52 (2011), 131-156 (with G. Khuskivadze and V. Paatashvili).

  211. Two-weighted norm inequalities for the double Hardy transforms and strong fractional maximal functions in variable exponent Lebesgue spaces. “Spectral Theory, Function Spaces and Inequalities _ New Techniques and Recent Trends”. “Operator Theory: Advances and Applications” (The volume is dedicated to Professor D. E. Edmunds and W. D. Evans), 105-124, Vol. 219, Birkhäuser, Basel, 2012 (with A. Meskhi).

  212. *Trace inequalities for integral operators with fractional order in grand Lebesgue spaces. Studia Mathematica, 210(2012), 159-176 (with A. Meskhi) .

  213. Singular integrals and strong maximal functions in weighted grand Lebesgue spaces, Nonlinear Analysis, Function Spaces and Applications, vol. 9, Proceedings of the International School held in Třešt, September 11-17, 2010, Edited by Jiři Rakosnik, Institute of Mathematics, Academy of Sciences of the Czech Republic, 2011.

  214. Approximation by trigonometric polynomials of functions having $(\alpha, \psi)$-derivatives in weighted variable exponent Lebesgue spaces, Journal of Mathematical Sciences, 184 (2012), No. 4, 371-382 (with R. Akgün).

  215. Some approximation problems for $(\alpha, \psi)$-differentiable functions in weighted variable exponent Lebesgue spaces, Journal of Mathematical Sciences, 186 (2012), No. 2, 139-152 (with R. Akgün).  

  216. *The refined estimates of trigonometric approximation for functions with generalized derivatives in weighted variable exponent Lebesgue spaces. Georgian Math. J. 19 (2012), No. 4, 611-626 (with R. Akgün).

  217. On the approximation of periodic functions within the frame of grand Lebesgue spaces, Bull. Georgian Nat. Acad. Sci. 6 (2012), No. 2, 11-16 (with N. Danelia).

  218. *Riesz type potential operators in generalized grand Morrey spaces. Georgian Math. J.  20 (2013), no. 1, DOI 10.1515/gmj-2-13-0209 (with A. Meskhi and H. Rafeiro).

  219. The Riemann and Dirichlet problem with data from grand Lebesgue spaces, Advances in Harmonic Analysis and Operator Theory, Operator Theory: Advances and Applications 229 (2013), 233-251 (with V. Paatashvili).

  220. *Potentials with product kernels in grand Lebesgue spaces. One weighted criteria. Lithuanian Math. J.  53 (2013), No. 1, 27-39 (with A. Meskhi).

  221. *Positive kernel operators in $L^{p(x)}$ spaces. Positivity 17 (2013), no. 4, 1123-1140 (with A. Meskhi and M. A. Zaighum).

  222. *Criteria for the boundedness and compactness of kernel operators in variable exponent amalgam spaces, J. Inequalities Appl. 2013, 2013:173, 1-27;DOI 10.1186/1029-242X-2013-173, 2013 (with A. Meskhi and M. A. Zaighum).

  223. *Two-weight norm estimates for maximal and Calderón-Zygmund operators in variable exponent Lebesgue spaces. Georgian Math. J.  20 (2013),  No. 3, 547-572  (with A. Meskhi and M. Sarwar).

  224. *Boundedness of commutators of singular and potential operators in generalized grand Morrey spaces and some applications, Studia Math. 217 (2013), No. 2, 159-178 (with A. Meskhi and H. Rafeiro).

  225. *Boundedness criteria for the majorants of the Cesáro summation means in weighted variable exponent Lebesgue spaces. Georgian Math. J. 20 (2013), No. 4, 721-727 (with I. Nanobashvili).

  226. One-weight weak type estimates for fractional and singular integrals in grand Lebesgue spaces. Banach Center Publications, Institute of Mathematics, Polish Academy of Sciences 102 (2014), 131-141 (with A. Meskhi).

  227. *Estimates for nondivergence elliptic equations with VMO coefficients in generalized grand Morrey spaces, Complex Variables and Elliptic Equations, 59 (2014), No 8, 1169-1184 (with A. Meskhi and H. Rafeiro).

  228. *Grand Bochner-Lebesgue spaces. Journal of Functional Analysis, 266 (2014), No 4, 2125-2136 (with A. Meskhi and H. Rafeiro).

  229. *On the boundedness of multi-linear fractional integrals. Nonlinear Analysis, Theory, Methods and Applications, 94 (2014), 142-147 (with M. Mastylo and A. Meskhi).

  230. The Dirichlet and Riemann-Hilbert problems in Smirnov classes with variable exponent in doubly-connected domains. J. Math. Sci. 198 (2014), No 6, 735-746 (with V. Paatashvili).

  231. Some fundamental inequalities for trigonometric polynomials in imbeddings of grand Besov spaces. Proc. A. Razmadze Math. Inst. 165 (2014), 105-116 (with A. Meskhi).

  232. *Two-weight norm estimates for sublinear integral operators in variable exponent Lebesgue spaces. Studia Sci. Math. Hungar. 51 (2014), No 3, 384-405 (with A. Meskhi).

  233. *Maximal and Calderón–Zygmund operators in grand variable exponent Lebesgue spaces. Georgian Math. J. 21  (2014), No. 4, 447-461 (with A. Meskhi).

  234. *The multisublinear maximal type operators in Banach function lattices. J. Math. Analysis & Appl. 421, No. 1, 656-668 (with M. Mastylo and A. Meskhi).

  235. *Fractional integral operators between Banach function lattices. Nonlinear Anal., Theory Methods Appl. 117 (2015),148-158 (with A. Meskhi and M. Mastylo).

  236. *On weighted Bernstein type inequality in variable exponent grand Lebesgue spaces. Mathematical Inequalities & Applications 18 (2015), No. 3, 991-1002 (with A.Meskhi).

  237. *Two-weight estimates for multilinear fractional integrals in classical Lebesgue spaces. Fractional Calculus and Applied Analysis, Springer 18 (2015), No.5, DOI:10.1515/fca-2015-0066

     (with M. Mastylo and A. Meskhi).

  238. The inverse inequalities of trigonometric approximation in weighted variable exponent. Lebesgue spaces with different space norms. Bull. Georgian Nat. Academy. Sci. 9 (2015), No. 1, 9-11.

  239. Sharp weighted bounds for multiple integral operators. Trans. A. Razmadze Math. Inst. 170 (2016),75-90 (with A. Meskhi and A. Zaighum).

  240. *Approximation by trigonometric polynomials in the framework of grand variable exponent Lebesgue space. Georgian Math. J. 23 (2016), no. 1, 43-53 (with N. Danelia).

  241. *Weighted extrapolation in Ivaniec-Sbordone spaces. Application to the integral operators and the approximation theory. Proc. Steklov Inst. Mat.  293 (2016), 161-185. Original text published in Trudy Mat. Inst. Steklov. 203 (2016), 1-26 (with A. Meskhi).

  242. *Multilinear integral operators in weighted grand Lebesgue spaces. Fractional Calculus and Applied Analysis 19 (2016), no. 3, 1-29 (with A. Meskhi and M. Mastyło).

  243. The Riemann-Hilbert problem in the class of Cauchy type integrals with densities of  grand Lebesgue spaces. Trans. A. Razmadze Math. Inst. 170 (2016), 208-211  (with A. Meskhi and V. Paatashvili).

  244. Generalized singular integrals on Carleson curves in weighted grand Lebesgue spaces. Trans. A. Razmadze Math. Inst. 170 (2016), 212-214 (with A. Meskhi and V. Paatashvili).

  245. *Sublinear operators in generalized weighted Morrey spaces. Dokl. Math. 94 (2016), No. 2, 558-560 (with A. Meskhi and H. Rafeiro).

  246. The Riemann boundary value problem in the class of Cauchy type integrals with densities of grand variable exponent Lebesgue spaces. Georgian Math. J. 23 (2016), no. 4, 551-558   (with A. Meskhi and V. Paatashvili).

  247. *Sharp weighted bounds for one-sided operators. Georgian Math. J. 24 (2017), no. 2, 227–240 (with A. Meskhi and M. Zaighum).

  248. *Hardy-Littlewood maximal operator in weighted grand variable exponent Lebesgue spaces. Mediterr. J. Math. 14 (2017), no. 3, 14:118 (with A. Fiorenza and A. Meskhi).

  249. *On the Riemann-Hilbert boundary value problem for generalized analytic functions in the framework of variable exponent spaces. Math. Methods Appl. Sci. 40 (2017), no. 18, 7267-7286  (with V.Paatashvili); DOI: 10. 1002/mma 4528.

  250. *Boundedness of sublinear operators in weighted grand Morrey spaces. Math. Notes 102 (2017), 664-676 (with A. Meskhi and H. Rafeiro).

  251. *The boundedness of sublinear operators in weighted Morrey spaces defined on spaces of homogeneous type. In: P. Jain, H. J. Schmeisser (eds.), Function Spaces and Inequalities. Springer Proceedings in Mathematics & Statistics, vol. 206, pp. 193-211, Springer, Singapore, 2017 (with A. Meskhi).

  252. *Riemann-Hilbert problem in the class of Cauchy-type integrals with densities of grand Lebesgue spaces. Complex Variables and Elliptic Equations 63 (2018), no.9, 1233-1257  (with V. Paatashvili); DOI/10.1080/17475933.2017./357705.

  253. *Nonlinear harmonic analysis integral operators in weighted grand Lebesgue spaces and applications. Annals of Functional Analysis 9 (2018), no.3, 413-425 (with A. Fiorenza); DOI: 1215/20088752-2017-0056.

  254. *Sharp weighted bounds for fractional integrals via the two-weight theory. Banach J. Math. Analysis 12 (2018), no. 3, 673-692 (with A. Meskhi and M. A. Zaighum);  doi:10.2018/17358787-2017-0053.

  255. *Extrapolation results in grand Lebesgue spaces defined on product sets. Positivity 22 (2018), no. 4, 1143-1163 (with A.Meskhi); DOI:10.1007/s117018-0564-7, 1-21.

  256. *One sided operators in grand variable exponent Lebesgue spaces. Zeitshrift für Analysis und ihre Anwendungen 37 (2018), no. 3, 251-275 (with A. Meskhi).

  257. *Extrapolation in Grand Lebesgue Spaces with $A_\infty$ Weights. (Russian) Mat. Zametki 104 (2018), no. 4, 539-551 (Engl. transl: Math. Notes 104 (2018), no. 4,  518-529) (with A. Meskhi). 

  258. *Sobolev-type inequalities for potentials in grand variable exponent Lebesgue spaces. Math. Nachr. 292 (2019), no. 10, 2174-2188; DOI: 10.1002/mana.201800239 (2019) (with D. Edmunds and A. Meskhi).

  259. *Weighted extrapolation in grand Morrey spaces and applications to partial differential equations. Atti Accad. Naz. Lincei Rend. Lincei Mat. Appl. 30 (2019), no. 1, 67-92 (with A.Meskhi and A.Raguza); Doi 10.471/ RLM /836.

  260. *Commutators of sublinear operators in grand Morrey spaces. Studia Sci. Math. Hungarica 56 (2019), no. 2, 211-232 (with A. Meskhi and H. Rafeiro).

  261. *The measure of non-copactness of multsublinear operators. J. Nonlinear Anal. Appl. 188 (2019), 70-79 (with A. Meskhi and M. Mastylo).

  262. *Compactness criteria for fractional integral operators. Fractional Calculus and Applications 22 (2019), no. 5, 1269-1283 (with M. Mastylo and A. Meskhi).

  263. Maximal and Calderon-Zygmund operators in weighted grand variable exponent spaces. Trans. A. Razmadze Math. Inst. 173 (2019), 127-131 (with A. Meskhi).

  264. Angular trigonometric approximation in the framework of new scale of function spaces. Trans. A. Razmadze Math. Inst. 173 (2019), 133-136 (with Ts. Tsanava).

  265. *Weighted grand Lebesgue space with mixed norm and integral operators. (in Russian)  Doklady RAN 489 (2019), no. 4; English transl.: Doklady Mathematics 100 (2019), no. 3, 1-4.

  266. *On the boundedness of multilinear fractional integral operators. J. Geom. Anal. 30 (2020), 667-679 (with M. Mastyło and A. Meskhi); http://doi.org/10.1007/s12220-oi9-00 159-6. 

  267. *Extrapolation in weighted classical and grand Lorentz spaces. Application to the boundedness of integral operators. Banach J. Math. Anal. 14 (2020), no. 3, 1111-1142 (with A. Meskhi); DOI:10.1007/s 43037-020-00054-1.

  268. A note on the multiple fractional integrals defined on the product of nonhomogeneous measure spaces. Trans. A. Razmadze Math. Inst. 174 (2020), no. 2, 257-259 (with Ts. Tsanava).

  269. On the boundedness of multiple Cauchy singular and fractional integrals defined on the product of rectifiable curves. Trans. A. Razmadze Math. Inst. 174 (2020), no. 2, 251-255.

  270. *Weighted grand mixed-norm Lebesgue spaces and boundedness criteria for integral operators. Georgian Math. J. 27 (2020), no. 4, 577-583; DOI:10.1515/GMJ-2020-2071.

  271. *Trace inequalities for fractional integrals in mixed-norm grand Lebesgue spaces. Fract. Calc. Appl. Anal. 23 (2020), no. 5,  1452-1471 (with A. Meskhi); DOI:10.1515/fc/2020.

  272. *Calderon-Zygmund singular operators in extrapolation spaces. J. Funct. Anal. 279 (2020), no. 10, 108735, 21 pp. (with M. Mastylo and A. Meskhi); https://doi.org/10.1016/jfa.2020.108 735.

  273. *Weighted Sobolev inequality in grand mixed norm Lebesgue spaces. Positivity 25 (2021), no. 1, 273-288 (with A.Meskhi); http//doi.org/10.1007/s 11117-020-00/764-8 (2020).

  274. *Boundedness of integral operators in generalized weighted Lebesgue spaces with non-doubling measures. Mediterr. J. Math.  18 (2021), no. 2, 50 (with A. Meskhi); http:doi.org/10.1007/s 00009-020-01694-1

  275. *Singular integral operators in some variable exponent Lebesgue spaces. Georgian Math. J. (with A. Mastylo and A. Meskhi); DOI:10.1515/GMJ-2020-2065.

  276. *On integral operators in weighted grand Lebesgue spaces of Banach-valued functions. Mathematical Methods in the Applied Sciences, https://doi.org/10.1002/mma.6779, First published: 30 July 2020.

  277. *On the boundedness of integral operators in weighted grand Morrey spaces. Proc. Steklov Inst. Math. 312 (2021), no. 1, 194-206 (with A. Meskhi).

  278.  Weighted extrapolation in mixed norm function spaces, Trans. A. Razmadze Math. Inst. 175 (2021), no. 2, 287-291 (with A. Meskhi).

  279. *Fractional integrals with measures in grand Lebesgue and Morrey spaces. Integral Transforms and Special Functions (with A. Meskhi), https://doi.org/10.1080/10652469.2020.1833003.

  280. *Maximal and singular integral operators in weighted grand variable Lebesgue spaces. Annals of Functional Analysis (with A.Meskhi); DOI 10.1007/s43034-021-00135-8.

  281. *Embeddings in grand variable exponent function spaces. Results of Math. (with D. E. Edmunds and A. Meskhi); DOI 10.1007/s00025-021-01450-1.

  282. *Extrapolation and boundedness in grand variable exponent Lebesgue spaces without assuming the log-Holder condition and application. J. Fourier Anal. Appl. (with A. Meskhi), DOI: 10.1007/s00041-022-09919-5.

  283. *Rubio de Francia's weighted extrapolation in mixed norm spaces and applications. Math. Nachr. (with A. Meskhi), DOI: 10.1002/mana.202100244.

 

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