## Professor Vakhtang Paatashvili

(22.VI. 1936 - 10.XI.2017)

### Education and Scientific Degrees

 1955 - 1960 Tbilisi State University 19.03.1966 Candidate of Physical & Mathematical Sciences (Ph. D. in Mathematics) 17.07.1985 Dr. Sci. (Phys. & Math.)

### Positions Held and Academic Experience

 01/06/1963 - 16/01/1969 Junior Researcher at A. Razmadze Mathematical Institute of Georgian Academy of Sciences 16/01/1959 - 01/11/1986 Senior Researcher at A. Razmadze Mathematical Institute of Georgian Academy of Sciences 01/11/1986 - 01/11/2006 Leading Researcher at A. Razmadze Mathematical Institute of Georgian Academy of Sciences 01/11/2006 - 30/11/2017 Senior Researcher at A. Razmadze Mathematical Institute Tbilisi State University

 1982 - 2006 Member of Scientific Council at A. Razmadze Mathematical Institute of Georgian Academy of Sciences 1999 - 2015 Member of Editorial Board of "Proceedings of A. Razmadze Mathematical Institute" 2015 - 2017 Member of Editorial Board of "Transactions of A. Razmadze Mathematical Institute"

### List of Main Publications

1. A discontinuous problem if linear conjugation with summable coefficients. (Russian) Soobshch. Akad. Nauk Gruz. SSR 24 (1964), 519-524.
2. On a discountinuous problem of linear conjugacy. (Russian) Soobshch. Akad. Nauk Gruz. SSR 36 (1964), 539-544.
3. On a linear .conjugacy problem in the case of a denumerable set of closed contours. (Russian) Soobshch. Akad. Nauk Gruz. SSR 37 (1965), 31-36.
4. The problem of linear conjugacy in the case of the infinite line. (Russian) Soobshch. Akad. Nauk Gruz. SSR 47 (1967), 7-12.
5. The linear problem of conjugacy in the case of a denumerable set of closed contours. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 34 (1968), 103-122.
6. Singular Cauchy integrals. (Russian) Soobshch. Akad. Nauk Gruz. SSR 53 (1969), 529-532.
7. A certain property of a singular Cauchy integral. (Russian) Soobshch. Akad. Nauk Gruz. SSR 61 (1971), 15-16.
8. On belonging to the classes EP of Analytic functions which are representable by a Cauchy type integral. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 42 (1972), 87-94.
9. On the boundedness of Cauchy singular integrals in weight Lebesgue spaces. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 43 (1973), 111-119.
10. On the boundary value problem of linear conjugation with measurable coefficients (with V. Kokilashvili). (Russian) Dokl. Akad. Nauk SSSR 224 (1975), 1008-1011; English transl.: Sov. Math. Dokl. 16 (1975), 1339-1343.
11. Certain properties of singular integrals and of Cauchy type integrals. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 47 (1975) (Sb. Rab. Teor. Funkcii 6), 34-52.
12. Correction (with V. Kokilashvili). (Russian) Dokl. Akad. Nauk SSSR 227 (1976), 776.
13. Linear integral equations with p-mean singular integral. (Russian) Dokl. Akad. Nauk SSSR 231 (1976), 1293-1295; English transl.: Sov. Math. Dokl. 17(1976) (1977), 1724-1727.
14. Some properties of the Cauchy singular integral along open curves. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 53 (1976), 62-72.
15. A boundary value problem of linear conjugation with measurable coefficients (with V. Kokilashvili). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 55 (1977), 59-92.
16. A problem of linear conjugation with measurable coefficients for a certain curves (with V. Kokilashvili). (Russian) Soobshch. Akad. Nauk Gruz. SSR 91 (1978), 25-27.
17. On the boundedness of Cauchy singular operator in Lp-spaces. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 58 (1978), 187-196.
18. On a discountinuous problem o linear conjugation with summable coefficients for one class of curves (with V. Kokilashvili). (Russian) Soobshch. Akad. Nauk Gruz. SSR 91 (1978), No. 1, 25-27.
19. A singular Cauchy integral on a countable set of closed contours. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 65 (1980), 122-130.
20. Discoutinuous problems in linear conjugation and singular integral equations (with V. Kokilashvili). (Russian) Differentsial'nye Uravneniya 16 (1980), 1650-1659; English transl.: Differ. Equations 16 (1981), 1067-1075.
21. On the singular Cauchy operator on a countable set of concentric circles (with G. Khuskivadze). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 69 (1982), 80-92.
22. On the boundedness of the singular Cauchy operator in Lebesgue spaces in the case of non-smooth contours (with G. Khuskivadze). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 69 (1982), 93-107.
23. A discountinuous Riemann-Hilbert problem. (Russian) Reports of enlarged session of the seminar of  I. Vekua Institute of Appl. Math. 1 (1985), 168-170.
24. The homogeneous discountinuous problem of linear conjugation in case of a countable connected domain. (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 82 (1986), 127-141.
25. On the derivative of conformal mapping (with G. Khuskivadze). (Russian) Soobshch. Akad. Nauk Gruz. SSR 127 (1987), 473-475.
26. On the Noether property of linear singular integral equations in weighted Lebesgue spaces. (Russian) Z. Anal. Anwend. 8 (1989), No. 3, 231-236.
27. An approximate solution of a class of Noether equations (with A. Saginashvili). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 88 (1989), 15-26.
28. On an aplication of the problem of linear conjugation to the study of properties of a conformal mapping (with G. Khuskivadze). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze 88 (1989), 27-40.
29. On Riemann-Hilbert problem in domain with non-smooth boundary (with G. Khuskivadze). (Russian) Reports of enlarged session of the seminar of I. Vekua Institute of Appl. Math. 5 (1990), No. 1,  153-156.
30. On Dirichlet problem for harmonic functions in domain with piecewise smooth boundary (with G. Khuskivadze). (Russian) Reports of enlarged session of the seminar of I. Vekua Institute of Appl. Math. 7 (1992), No. 1.
31. Riemann-Hilbert problem in the domain with nonsmooth boundary (with G. Khuskivadze). (Russian) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Gruzii 106(1993), 105-122.
32. On the boundedness of Cauchy singular operator from the space Lp to Lq, p > q ³ 1 (with G. Khuskivadze). Georgian Math. J. 1(1994), No. 4, 395-403.
33. On the Riemann-Hilbert problem in the domain with non-smooth boundary (with V. Kokilashvili). Georgian Math. J. 4(1997), No. 3, 279-302.
34. Neumann problem in the class of harmonic functions in domain with a piecewise-Lyapunov boundary (with V. Kokilashvili). Mem. Differential Equations Math. Phys. 12(1997), 114-121.
35. On the inclusion of the Cauchy type integrals into the Smirnov's classes (with G. Khuskivadze). Proc. Razmadze Math. Inst. 114(1997), 71-79.
36. On conformal mapping of simply connected domains with a piece-wise smooth boundary (with G. Khuskivadze). Proc. Razmadze Math. Inst. 114(1997), 81-88.
37. On the continuity of the Cauchy operator from the space Lp(G) to Lq(G) for p > q³ 1 (with G. Khuskivadze). Proc. Razmadze Math. Inst. 114(1997), 124-126.
38. On the conformal mapping of a circle onto a domain with an arbitrary piecewise smooth boundary (with G. Khuskivadze). Proc. A. Razmadze Math. Inst. 116(1998), 123-132.
39. Boundary value problems for analytic and harmonic functions in domains with non-smooth boundaries. Applications to conformal mappings (with G. Khuskivadze and V. Kokilashvili). Mem. Differential Equations Math. Phys. 14(1998), 1-195.
40. On conformal mapping of the domain with a piecewise smooth curve on the same domain (with G. Khuskivadze). Reports of enlarged session of the seminar of I. Vekua Institute of Appl. Math. 13(1998), No. 1, 20-22.
41. On harmonic functions from Smirnov's class (with Z. Meshveliani). Proc. A. Razmadze Math. Inst. 121(1999), 159-160.
42. Riemann-Hilbert problem in the domains with piecewise smooth boundaries (with V. Kokilashvili). (Russian) Bull. Georgian Acad. Sci. 159 (1999), No. 1, 11-14.
43. On the Dirichlet and Neumann problems in the domains with piecewise smooth boundaries (with V. Kokilashvili). (Russian) Bull. Georgian Acad. Sci. 159 (1999), No. 2, 181-183.
44. On Smirnov classes of harmonic functions and the Dirichlet problem (with Z. Meshveliani). Proc. A. Razmadze Math. Inst. 123(2000), 61-91.
45. On the boundedness of Cauchy singular integral operator (with G. Khuskivadze). Proc. A. Razmadze Math. Inst. 124(2000), 107-114.
46. On a Dirichlet problem in Smirnov classes of harmonic functions (with Z. Meshveliani). Proc. A. Razmadze Math. Inst. 126(2001), 53-57.
47. On a representation of the derivatives of conformal mappings (with G. Khuskivadze). Georgian Math. J. 8(2001), No. 3, 513-520.
48. A problem of linear conjugation for analytic functions with boundary values from the Zygmund class (with V. Kokilashvili). Georgian Math. J. 9 (2002), 309-324.
49. Zaremba's problem in one class of harmonic functions (with G. Khuskivadze). Proc. A. Razmadze Math. Inst. 132 (2003), 143-147.
50. The Dirichlet problem for harmonic functions with boundary values from Zygmund classes (with V. Kokilashvili). Georgian Math. J. 10 (2003), No. 3, 531-542.
51. Boundary value problems for analytic and harmonic functions of Smirnov classes in the domains with nonsmooth boundaries (with V. Kokilashvili and Z. Meshveliani). Proc. Conf. in Madeira in honour of Prof. G. Litvinchuk, Kluwer Academic Publishers, 2003.
52. On Zaremba's boundary value problem for harmonic functions of Smirnov classes (with G. Khuskivadze). Mem. Differential Equations Math. Phys. 32 (2004), 29-58.
53. On a property of harmonic functions from the Smirnov class (with G. Khuskivadze). Mem. Differential Equations Math. Phys. 33 (2004), 87-94.
54. On the conformal mapping of simply connected domains with non-Jordan boundaries (with G. Khuskivadze). Proc. A. Razmadze Math. Inst. 136 (2004), 85-90.
55. On the Dirichlet problem for harmonic functions of Smirnov classes in doubly-connected domains (with G. Khuskivadze). Proc. A. Razmadze Math. Inst. 136 (2004), 141-144.
56. On a property of harmonic functions from the Smirnov class. Mem. Differential Equations Math. Phys. 33 (2004), 87-94.
57. One necessary condition for the continuity of a singular Cauchy operator in Lebesgue spaces with a variable exponent. Proc. A. Razmadze Math. Inst. 138 (2005), 115-118.
58. Boundary value problems for analytic functions in the class of Cauchy-type integrals with density in $L^{p(·)}(\Gamma)$ (with V. Kokilashvili and S. Samko). Bound. Value Probl. 2005, no. 1, 43-71.
59. On Hardy classes of analytic functions with a variable exponent (with V. Kokilashvili). Proc. A. Razmadze Math. Inst. 142 (2006), 134-137.
60. V. Zaremba's problem for harmonic functions from the Smirnov's weighted classes in domains with piecewise Lyapunov boundaries (with G. Khuskivadze). Proc. A. Razmadze Math. Inst. 142 (2006), 129-133.
61. Zaremba's problem in Smirnov class of harmonic functions in domains with piecewise-Lyapunov boundaries (with G. Khuskivadze). Proc. A. Razmadze Math. Inst. 143 (2007), 79-94.
62. On the Riemann-Hilbert problem in weighted classes of Cauchy type integrals with density from $L^{P(\cdot)}(\Gamma)$ (with V. Kokilashvili). Lect. Notes TICMI 8 (2007), 43-52.
63. On the Dirichlet problem for harmonic functions from Smirnov classes in doubly-connected domains (with G. Khuskivadze). Proc. A. Razmadze Math. Inst. 144 (2007), 41-60.
64. The Riemann-Hilbert problem in domains with piecewise-smooth boundaries in classes of Cauchy type integrals with density from $L^{p(\cdot)}(\Gamma)$ (with V. Kokilashvili). Proc. A. Razmadze Math. Inst. 145 (2007), 103-108.
65. The Dirichlet problem for harmonic functions of Smirnov classes in doubly-connected domains with arbitrary piecewise smooth boundaries (with G. Khuskivadze). Proc. A. Razmadze Math. Inst. 146 (2008), 67-78.
66. On the convergence of sequences of functions in Hardy classes with a variable exponent (with V. Kokilashvili). Proc. A. Razmadze Math. Inst. 146 (2008), 124-126.
67. The Haseman boundary value problem in classes of functions representable by the Cauchy type integral with density in $L^{p(\cdot)}$. Proc. A. Razmadze Math. Inst. 150 (2009), 142-149.
68. The Haseman's problem with a piecewise-continuous coefficient in classes of functions representable by the Cauchy type integral with density from $L^{p(\cdot)}(\Gamma)$. Proc. A. Razmadze Math. Inst. 154 (2010), 111-126.
69. Zaremba's boundary value problem in the Smirnov class of harmonic functions in domains with piecewise-smooth boundaries (with G. Khuskivadze). Mem. Differential Equations Math. Phys. 51 (2010), 73-91.
70. The Dirichlet problem for harmonic functions from variable exponent Smirnov classes in domains with piecewise smooth boundary (with V. Kokilashvili). Problems in mathematical analysis. No. 52. J. Math. Sci. (N.Y.) 172 (2011), no. 3, 401-421.
71. The Dirichlet problem for harmonic functions from variable exponent Smirnov classes in domains with a piecewise smooth boundary (with V. Kokilashvili). Proc. A. Razmadze Math. Inst. 155 (2011), 154-157.
72. The Dirichlet problem for variable exponent Smirnov class harmonic functions in doubly-connected domains (with G. Khuskivadze and V. Kokilashvili). Mem. Differential Equations Math. Phys. 52 (2011), 131-156.
73. Weighted Hardy and Smirnov classes and the Dirichlet problem for a ring within the framework of variable exponent analysis (with V. Kokilashvili). Complex Variables and Elliptic Equations 56 (2011), No. 10-11, 955-973.
74. On some properties of analytic functions from Smirnov class with a variable exponent. Mem. Differ. Equ. Math. Phys. 56 (2012), 73-88.
75. On the factorization of bounded measurable functions in the classes of Cauchy type integrals with density from $L^{p(\cdot)}(\Gamma;\omega)$. Georgian Math. J. 20 (2013), no. 4, 753-774.
76. Variable exponent Smirnov classes of generalized analytic functions. Proc. A. Razmadze Math. Inst. 163 (2013), 93-110.
77. On the Riemann problem with a measurable coefficient in the class of Cauchy type integrals with density from $L^{p(t)}$. Proc. A. Razmadze Math. Inst. 162 (2013), 151-155.
78. The Riemann and Dirichlet problem with data from grand Lebesgue spaces (with V. Kokilashvili). Advances in Harmonic Analysis and Operator Theory, Operator Theory: Advances and Applications 229 (2013), 233-251.
79. The Riemann problem and linear singular integral equations with measurable coefficients in Lebesgue type spaces with a variable exponent. Mem. Differ. Equ. Math. Phys. 61 (2014), 103-145.
80. The Noetherity criteria of the Riemann-Hilbert problem for variable exponent Smirnov classes in domains with piecewise smooth boundaries. Proc. A. Razmadze Math. Inst. 164 (2014), 130-135.
81. The Riemann-Hilbert problem in Smirnov class with a variable exponent and an arbitrary power weight. Proc. A. Razmadze Math. Inst. 165 (2014), 117-133.
82. The Dirichlet and Riemann-Hilbert problems in Smirnov classes with variable exponent in doubly connected domains (with V. Kokilashvili). J. Math. Sci. (N.Y.) 198 (2014), no. 6, Problems in mathematical analysis. No. 75 (Russian), 735-746.
83. On variable exponent Hardy classes of analytic functions. Proc. A. Razmadze Math. Inst. 169 (2015), 93-103.
84. The Riemann boundary value problem in variable exponent Smirnov class of generalized analytic functions. Proc. A. Razmadze Math. Inst. 169 (2015), 105-118.
85. Smirnov classes of analytic functions with variable exponent in multiply connected domains. Bull. Georgian Natl. Acad. Sci. (N.S.) 9 (2015), no. 1, 16-23.
86. The Riemann-Hilbert problem in the class of Cauchy type integrals with densities of grand Lebesgue spaces with V. Kokilashvili and A. Meskhi). Trans. A. Razmadze Math. Inst. 170 (2016), no. 2, 208-211.
87. Generalized singular integral on Carleson curves in weighted grand Lebesgue spaces (with V. Kokilashvili and A. Meskhi). Trans. A. Razmadze Math. Inst. 170 (2016), no. 2, 212-214.
88. The Riemann boundary value problem in the class of Cauchy type integrals with densities of grand variable exponent Lebesgue spaces (with V. Kokilashvili and A. Meskhi). Georgian Math. J. 23 (2016), no. 4, 551-558.
89. Certain properties of generalized analytic functions from Smirnov class with a variable exponent. Mem. Differ. Equ. Math. Phys. 69 (2016), 77-91.
90. Smirnov classes of analytic functions with variable exponent in multiply connected domains. Complex Var. Elliptic Equ. 61 (2016), no. 1, 29-41.
91. *Riemann-Hilbert problem in the class of Cauchy-type integrals with densities of grand Lebesgue spaces (with V. Kokilashvili). Complex Variables and Elliptic Equations, DOI/10.1080/17475933.2017./357705.
92. *On the Riemann-Hilbert boundary value problem for generalized analytic functions in the framework of variable exponent spaces (with V. Kokilashvili). Mathematical Methods in the Applied Sciences,  DOI: 10. 1002/mma 4528.

### Other Publications

1. On the occasion of Givi Khuskivadze's 80th birthday anniversary (with R. Bantsuri, N. Kekelidze, I. Kiguradze, V. Kokilashvili and T. Oziashvili). Mem. Differ. Equ. Math. Phys. 56 (2012), 1-7.

2. Revaz Bantsuri (with I. Kiguradze, V. Kokilashvili and N. Shavlakadze). Proc. A. Razmadze Math. Inst. 164 (2014), 1-3.

3. Revaz Bantsuri (with I. Kiguradze, V. Kokilashvili and N. Shavlakadze). Mem. Differ. Equ. Math. Phys. 61 (2014), 1-3.

4. On the occasion of Boris Khvedelidze's 100th birthday anniversary. Proc. A. Razmadze Math. Inst. 169 (2015), 1-7.