CURRICULUM VITAE

Prof. Dr. VAKHTANG KOKILASHVILI

Name Kokilashvili Vakhtang M.
Date of birth May 1, 1938
academic titles Corresponding member of the Georgian Academy of Sciences (1997), Dr. Sci. (Phys., Math.) (1981), Professor (1985)
Research interests Theory of Functions and Functional Analysis; Weight Theory of Integral Operators and Function Spaces; Applications to PDE
Pedagogical activities conducts from 1964. At present delivers lectures in the basic disciplines at Tbilisi State University, its Sukhumi Branch, Technical University, International Black Sea University
Scientific and public activities Deputy Director for Scientific Matters of A. Razmadze Mathematical Institute of the Georgian Academy of Sciences, Head of Mathematical Analysis Department since 07.07.1989 up to now. For 12 years conducts seminar in the Theory of Functions and Functional Analysis. A member of Editorial Board of  "Journal in Functional Spaces & Applications",  "International Journal in Mathematics, Algebra and Game Theory" (Nova Science Publishing, New York), "Georgian Mathematical Journal",  "Armenian J. Math.", "Georgian International Journal of Sciences and Technologies" and Scientific Editor of "Proceedings of A. Razmadze Mathematical Institute".
Additional main information Author of 163 scientific papers and five monographs. Scientific biography is put in the fifth Edition of the International Directory of Distinguished Leadership of American Biographical Institute, Inc. Endowed with A. Razmadze prize. A participant of ICM (Moscow 1966, Berlin 1998), ECM (Budapest 1996), ICM (Bejin 2002). A participant of several conferences, symposiums, workshops.
Visited Assistant 1965 Mickiewicz University in Poznan (Poland)
Visited Professor 1986, 1989, 1991 - Mathematical Institute in Prague
1993, 1997, 2000, 2003 - Sussex University (UK)
1994 - Mcmaster and Brock Universities (Canada)
1996 - Rudgers and Washington Universities (USA)
Address Nutsubidze Str. 60-15 380077, Tbilisi, Georgia
Contact address A. Razmadze Mathematical Institute
Georgian Academy of Sciences,
1, M. Aleksidze St., Tbilisi 0193
Georgia
Telephone 39.77.13 (home), 33.35.12 (Institute)
E-mail kokil@rmi.acnet.ge
kokil@imath.acnet.ge
.

(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, (to appear in 2012).

 

(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. im. 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, Moskwa, (1965), 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. im. Razmadze Akad. Nauk Gruzin. SSR 34(1968), 51-81.

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

  24. The direct theorem on mean approximations of analytic functions. (Russian) Dokl. Akad. Nauk Gruzin. SSR 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. im. Razmadze Akad. Nauk Gruzin. SSR 42(1972), 78-86.

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

  32. On boundary properties of functions of certain classes. (Russian) Trudy Tbiliss. Mat. Inst. im. 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. im. 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. im. 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. im. 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. im. 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. in 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. im. Razmadze Akad. Nauk Gruzin. SSR 58(1978), 134-149.

  47. On Calderon type singular integrals. (Russian) Trudy Tbiliss. Mat. Inst. im. 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. im. 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. im. 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: Colloqia 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. (Engiish transl.: Proc. Steklov Inst. Mat. 3(1984), 135-162.)

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

  59. On traces for weighted anisotropic Lizorkin-Triebel spaces. (Russian) Trudy Tbiliss. Mat. Inst. im. 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. im. 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. im. 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 translation: 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. im. 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. *Maximal functions in ji(L) classes. (Russian) Dokl. Akad. Nauk SSSR 314(1990), No. 3, 534-536; English transl.: Soviet Math. Dokl. 42(1991), No. 2, 488-490 (with A. Gogatishvili and M. Krbec).

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

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

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

  84. 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).

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

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

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

  88. Solution of Some Weight Problems. In: ``Function Spaces, Differential Operators and Nonlinear Analysis.'' Teubner-Texte zur Mathematik, 133, Teubner-Verlag, Leipzig, 1993, 264-273.

  89. Maximal functions, ji(L) classes and Carleson measures. Proc. A. Razmadze Math. Inst. 102(1993), 85-97 (with A. Gogatishvili, M. Krbec).

  90. 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).

  91. *Criteria General weak type inequalities for integral transforms with positive kernels. Georgian Math. J. 1(1993), No. 1, 9-29 (with I. Genebashvili and A. Gogatishvili).

  92. *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).

  93. *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.

  94. *Criteria of Weighted Inequalities in Orlicz Classes for Maximal Functions Defined on Homogeneous Type Spaces. Georgian Math. J. 2(1994), No. 6, 617-649 (with A. Gogatishvili).

  95. Criteria of weight inequalities for integral transforms defined on homogeneous type spaces. Topological vector spaces, algebras and related areas (Hamilton, ON, 1994), 251-262, Pitman Res. Notes Math. Ser., 316, Longman Sci. Tech., Harlow, 1994 (with A. Gogatishvili).

  96. *The necessary and sufficient conditions for weighted Orlicz class inequalities for maximal functions and singular integrals. I. Georgian Math. J. 2 (1995) No. 4, 361-384 (with A. Gogatishvili).

  97. Orlicz class inequalities for maximal functions and singular integrals. II. Georgian Math. J. 2 (1995), No. 5, 445-462 (with A. Gogatishvili).

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

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

  100. *Solution of two weight problem for integral transforms with positive kernels. Georgian Math. J. 3(1996), No. 4, 319-342 (with I. Genebashvili and A. Gogatishvili).

  101. *Criteria of two-weight strong type inequalities for fractional maximal functions defined on homogeneous type spaces. Georgian Math. J. 3(1996), No. 5, 319-342 (with A. Gogatishvili).

  102. *Criteria of two weighted inequalities for integral transforms with positive kernels and maximal functions. (Russian) Dokl. Akad. Nauk 351(1996), No. 4, 448-451 (with I. Genebashvili and A. Gogatishvili).

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

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

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

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

  107. 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).

  108. 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).

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

  110. 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).

  111. 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).

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

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

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

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

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

  117. 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).

  118. *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).

  119. 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).

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

  121. 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).

  122. *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).

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

  124. *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).

  125. 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).

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

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

  128. 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).

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

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

  131. *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). 

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

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

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

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

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

  137. 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).

  138. *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).

  139. *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).

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

  141. 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).

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

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

  144. *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).

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

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

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

  148. *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).

  149. 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.

  150. 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 ).

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

  152. 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).

  153. 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).

  154. * 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).

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

  156. 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).

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

  158. 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).

  159. *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).

  160. 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).

  161. *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).

  162. 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).

  163. 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).

  164. 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).

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

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

  167. 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).

  168. 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).

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

  170. 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).

  171. 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).

  172. *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).

  173. *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).

  174. *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).

  175. 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).

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

  177. *One-sided operators in Lp(x) spaces. Math. Nachr. 281(2008), n0. 11, 1525-1548 (with D. E. Edmunds and A. Meskhi).

  178. *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).

  179. *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).

  180. *The maximal operator in weighted variable exponent spaces in metric spaces. Georgian Math. J. 15(2008), #4, 683-712 (with S. Samko).

  181. Fractional, maximal and singular integral operators in variable Lorentz spaces. Fract. Calculus and Appl., 11(2008), #4, 407-420 (with L. Ephremidze and S. Samko).

  182. 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).

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

  184. 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).

  185. 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), N0. 4, 569-591 (with V. Paatashvili).

  186. Singular operators and Fourier multipliers in weighted Lebesgue spaces with variable exponent. (Russian) Vestnik St. Petersburg Univ. Mathematics, 41(2008), N0. 2, 134-144 (with S. Samko).

  187. *Riemann problem in the class of Cauchy-type integrals with density in . Doklady Mathematics, 78(2008), N0. 1, 510-513 (with V. Paatashvili and S. Samko).

  188. Boundedness of maximal and singular operators in Morrey spaces with variable exponent. Armenian J. Math. 1(2008), N0. 1, 18-28 (with A. Meskhi).

  189. On variable Hardy and Smirnov classes of analytic functions. Georgian International Journal of Sciences. Nova Science Publishers, Inc. 1(2008) N0. 2, 67-81 (with V. Paatashvili).

  190. *Two-weight estimates for strong fractional maximal functions and potentials with multiple kernels. J. Korean Math. Soc. 46(2009), N0. 3, 523-550 (with A. Meskhi).

  191. *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).

  192. On the Riemann-Hilbert-Poincaré problem and I. Vekua’s representation of holomorphic functions. Bull. of the Georgian National Academy of Sci. 3(2009), N0. 1, 25-29 (with V. Paatashvili).

  193. Maximal and potential operators in variable Morrey spaces defined on non-homogeneous spaces. Bull. of the Georgian National Academy of Sci. 2(2008), #3, 18-21 (with A. Meskhi).

  194. On the Calderon singular integrals in weighted variable Lebesgue spaces. Bull. of the Georgian National Academy of Sci. 2(2008), #4, 3-5.

  195. *On the approximation by trigonometric polynomials in weighted Lorentz spaces, Function Spaces & Appl. 8(2010), #1 (with Y. Ildirir).

  196. *The Riemann-Hilbert problem in domains with piecewise-smooth boundaries in classes of Cauchy type integrals with density from . Georgian Math. J. 16(2009), N0. 4 (with V. Paatashvili).

  197. 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).

  198. *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).

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

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

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

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

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

  204. *Maximal functions and potentials in variable exponent Morrey spaces with non-doubling measure. Complex Variables and Elliptic Equations, 55(2010), #8, 923-936 (with A. Meskhi)

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

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

  207. 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.

  208. Boundedness criteria for singular integrals in weighted grand Lebesgue spaces, Journal of Math. Anal. (Springer, New-York), 170(2010), # 1, 20-33.

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

  210. 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).

  211. *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).

  212. *On converse theorems of trigonometric approximation in weighted variable exponent Lebesgue spaces. Banach J. Math. Analysis, 5(2011), n 1, 70-82 (with R. Akgűn).

  213. 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).

  214. Two-weight inequalities for fractional maximal functions and singular integrals in $L^{p(\cdot)}$ spaces. J. Math. Sci. (Springer, New-York), 173(2011), n 6, 1-18 (with A. Meskhi).

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

  216. *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).

  217. *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).

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

  219. 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.

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

  221. 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).

  222. 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 (with A. Meskhi).

  223. Trace inequalities for integral operators with fractional order in grand Lebesgue spaces. (with A. Meskhi) (submitted).

  224. The Riemann and Dirichlet problem with data from grand Lebesgue spaces, Advances in Harmonic Analysis and Operator Theory. (with V. Paatashvili) (accepted).

  225. 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 Tiři Rakonik, Institute of Mathematics, Academy of Sciences of the Czech Republic, 2011.

  

  

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