AMIRAN

AMIRAN GOGATISHVILI

Monographs
1. I. Genebashvili, A. Gogatishvili, V. Kokilashvili and M. Krbec,

Weight theory for integral transforms on spaces of homogeneous type.
Pitman Monographs and Survey in Pure and Applied Mathematics 92, Longman, Harlow, 1998 . (MR 2003b:42002)

Research papers in academic journals

2. A. Gogatishvili. Fractional maximal functions with respect to the basis of the convex comperable sets in weighted Lebesgue spaces. (Russian. English and Georgian Summaries) Soobshch. Akad. Nauk Grusin. SSR, 129(1988), no. 2, 273-275. (MR 89g:42033)

3. A. Gogatishvili. Weighted inequalities for potentials in spaces of homogeneous type. (Russian. English and Georgian Summaries) Soobshch. Akad. Nauk Grusin. SSR, 129(1988), no. 3, 493--495. (MR 89i:42033)

4. A. Gogatishvili. Riesz transforms and maximal functions in $\varphi(L)$ classes. (Russian and Georgian Summaries) Soobshch. Akad. Nauk Grusin. SSR, 137(1990), no. 3, 489-492. (MR 91j:42009)

5. A. Gogatishvili, V.Kokilashvili and M.Krbec. Maximal functions in the classes $\varphi(L)$. (English, Russian original) Soviet Math. Dokl., 42(1991), no. 2, 488-490; translation from Dokl. Akad. Nauk SSSR 314(1990), no. 3, 534-536. (MR 92c:420018)

6. A. Gogatishvili. Maximal functions with respect to the basis of the comperable convex sets in weighted Lebesgue spaces. (Russian. English Summary) Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Grusin. SSR, 95(1990), 20-38. (MR 92h:42034)

7. A. Gogatishvili. Weighted inequalities for vector-valued fractional maximal functions (Russian. English Summary). Trudy Tbiliss. Mat. Inst. Razmadze Akad. Nauk Grusin. SSR, 98(1991), 9-18. (MR 94e:26037)

8. A. Gogatishvili. Weak type weighted inequalities for maximal functions with respect to the general basis. (Russian and Georgian Summaries) Soobshch. Akad. Nauk Grusin. SSR, 145(1992), no. 2, 249-252. (MR 94m:42040)

9. A. Gogatishvili. General weak--type inequalities for maximal operator and Riesz transforms. (Russian and Georgian Summaries) Soobshch. Akad. Nauk Grusin. SSR, 146(1992), no. 3, 497-500. (MR 94m:42041)

10. A. Gogatishvili. General weak type inequalities for maximal operators and singular integrals. (Georgian Summary) Proc. A.Razmadze Math. Inst., 101(1992), 47-63.
(MR 95e:42015)

11. A. Gogatishvili. Riesz transforms and maximal functins in $\varphi(L)$ classes. (Georgian Summary) Proc. A.Razmadze Math. Inst., 102(1993), 59-70. (MR 95d:42024)

12. A. Gogatishvili. Hilbert transform in Zygmund classes. (Georgian Summary) Proc. A.Razmadze Math. Inst., 102(1993), 71-84. (MR 95d:42065)

13. A. Gogatishvili, V. Kokilashvili and M. Krbec. Maximal functions, $\varphi(L)$ classes and Carleson measures. (Georgian Summary) Proc. A.Razmadze Math. Inst., 102(1993), 85-97. (MR 95e:42016)

14. A. Gogatishvili, L.Pick. Weighted inequalities of weak and extra-weak type for the maximal operator and Hilbert transform. Czechoslovak Math. J. 43(118) (1993), no.3, 547-566. (MR 95i:42013)

15. I. Genebashvili, A. Gogatishvili and V. Kokilashvili. Criteria of general weak type inequalities for integral transforms with positive kernels. (English and Georgian Summaries) Proc. Georgian Acad. Sci., Math.,1 (1993), no. 1, 11-35; Georgian Math. J. 1(1994), no. 1, 9--29. (MR 94j:42030)

16. A. Gogatishvili, Kokilashvili V. Criteria of weighted inequalities in Orlicz classes for maximal functions defined on homogeneous type spaces. (English and Georgian Summaries) Proc. Georgian Acad. Sci., Math., 1,6 (1993). pp. 721-755; (English Summary) Georgian Math. J. 1(1994), no. 6, 641--673. (MR 96b:42021)

17. A. Gogatishvili, V. Kokilashvili. Necessary and sufficient conditions for weigh\-ted Orlicz class inequalities for maximal functions and singular integrals. I (English Summary) Georgian Math. J. 2(1995), no. 4, 361-384. (MR 96g:42010)

18. A. Gogatishvili, V. Kokilashvili. Necessary and sufficient conditions for weigh\-ted Orlicz class inequalities for maximal functions and singular integrals. II (English Summary) Georgian Math. J. 2(1995), no. 5, 445-468. (MR 96m:42031)

19. I. Genebashvili, A. Gogatishvili and V. Kokilashvili. Solution of two-weight problems for integral transforms with positive kernel. (English Summary) Georgian Math. J. 3 (1996), no. 4, 319-342. (MR 97k:42029)

20. I. Genebashvili, A. Gogatishvili and V. Kokilashvili. Criteria of two-weighted inequalities for ntegral transforms with positive kernel and maximal functions. (English, Russian original) Dokl. Math. 54, no. 3, 895-898 (1996); translation from Dokl. Akad. Nauk RAN 351, no.4 , 448-451 (1996). (MR 98c:42030)

21. A. Gogatishvili and V. Kokilashvili. Criteria of strong type two-weighted inequalities for fractional maximal functions. (English Summary) Georgian Math. J. 3 (1996), no. 5, 423-446. (MR 98m:42020)

22. A. Gogatishvili. Two-weighted mixed inequalities in Orlicz classes for fractional maximal functions defined on homogeneous type spaces. (English and Georgian Summaries) Proc. A.Razmadze Math. Inst., 112(1997), 23-56. (MR 98m:42021)

23. A. Gogatishvili. Maximal functions and singular integrals on $L^{p,\varphi}$ spaces. Proc. A.Razmadze Math. Inst., 114(1997), 112-115. (MR 99i:46017)

24. A.Gogatishvili and J.Lang. The generalized Hardy operator with kernel and variable integral limits in Banach function spaces. J. Inequal. Appl., 4(1999), no.1, 1-16. (MR 2001f:47085)

25. A. Gogatishvili, Fractional maximal functions in weighted Banach function spaces, Real Analysis and Exchange, 25(1999/2000), no.1, 291-316. (MR 2001g:42029)

26. A.Gogatishvili and L.Pick, Duality principles and reduction theorems, Math. Inequal. Appl., (2000), no. 4, 539-558. (MR 2002c:46056)

<>27. A.Gogatishvili and T.Sobukawa, On the extrapolation estimates, Math. Inequal. Appl., 6(2003), no. 1, 97-104. (MR 2003k:46030)

28. A.Gogatishvili and L.Pick, Discretization and antidiscretization of rearrangement- invariant norms, Publ. Mat., 47(2003), no. 2, 311-358. (MR 2005f:46053)

29 A.Gogatishvili, A.Kufner, L.-E.Persson and A.Wedestig. An equivalence theorems for some scales of integral conditions related to Hardy's inequality with applications. Real Analysis and Exchange, 29(2003/04), no. 2, 867-880. (MR 2005f:26043)

30. A.Gogatishvili, J.S.Neves and B.Opic. Optimality of embeddings   of Bessel-potential-type spaces into Lorentz-Karamata spaces. Proc. Roy. Soc. Edinburgh Sec. A 134 (2004), no. 6, 1127 - 1147. (MR 2005h:46044)

31. A.Gogatishvili, B.Opic and W.Trebels. Limiting reiteration for real interpolation with slowly varying functions, Math. Nachr. 278(2005), no. 1-2, 86-107. (MR 2005k:46048)

32. A.Gogatishvili and P.Koskela. A non-doubling Trudinger inequality, Studia Math. 170 (2005), no. 2, 113-119. (MR 2007b:26041)

33. A.Gogatishvili, J.S.Neves and B.Opic. Optimality of embeddings of Bessel-potential-type spaces into generalized Hölder spaces, Publ. Mat. 49(2005), no. 2, 297-327. (MR 2006f:26002)

34. M.J.Carro, A.Gogatishvili, J.Martin and L.Pick. Function properties of rearrangement invariant spaces defined in term of oscillations, J. Funct. Anal. 229(2005), no. 2,
375-404. (MR 2006g:46051)

35. A.Gogatishvili, A.Kufner, L.-E.Persson and A.Wedestig. Compactness of the Hardy operator and its limiting case. Soochow J. Math. 32(2006), no. 1, 21-35.
(MR 2006m:26031)

36. A.Gogatishvili and L.Pick. Embeddings and duality theorems for weak classical Lorentz spaces, Canad. Math. Bull. 49(2006), no. 1, 82-95. (MR 2006k:26024)

37. A.Gogatishvili, B.Opic and L.Pick. Weighted inequalities for Hardy-type operators involving suprema, Collect. Math. 57(2006), no.3, 227-255. (MR 2007g:26019)

38. A.Gogatishvili and V.I.Ovchinnikov. The optimal embedding for the Calderon type spaces and the J-method spaces, Vestnik VGU, Ser. Phys. Math. 2006. no. 1, p.145-151.

39. A.Gogatishvili, J.S.Neves and B.Opic. Sharpness and non-compactness of embeddings of Bessel-potential-type spaces, Math. Nachr. 280(2007), no. 9-10, 1083-1093. (MR2334661)

40. A.Gogatishvili, M.Johansson, C.A.Okpoti and L.-E.Persson. Characterization of embeddings in Lorentz spaces using a method of discretization and anti-discretization, Bull. Austral. Math. Soc. 76(2007), no. 1, 69-92. (MR2343440)

41. A.Gogatishvili and L.Pick. A reduction theorem for supremum operators, J. Comput. Appl. Math.   208(2007), no.1, 270-279. (MR2347749)

42. A.Gogatishvili and V.I.Ovchinnikov. Interpolation orbits and optimal Sobolev's embeddings, J. Funct. Anal. 253(2007) no. 1, 1-17. (MR2362416)

43. A.Gogatishvili, W.D.Evans and   B.Opic. The reverse Hardy inequality with measures, Math. Inequal. Appl. 11 (2008), no. 1, 43-74. (MR2376257)

44 A.Gogatishvili, K.Kuliev and G.Kulieva. Some conditions characterizing the "Reverse" Hardy inequality, accepted in Real Analysis and Exchange, 33(2007/2008), no. 1,

45. M. Carro, A. Gogatishvili, J. Martin, L. Pick. Weighted inequalities involving two Hardy operators with applications to embeddings of function spaces, J. Operat. Theor 59(2008).

Papers accepted for publication

46. A.M.Caetano,   A.Gogatishvili and B.Opic Sharp embeddings of Besov spaces involving only logarithmic smoothness, Academy of Sciences of the Czech Republic, Institute of Mathematics. Preprint no. 168, 2007, 31 pages, accepted in J. Approx. Theory

47. W. D. Evans, A. Gogatishvili and B. Opic. The $\rho$-quasiconcave functions and weighted inequalities,

Preprints and Papers submitted   for publication

48. A.Gogatishvili, J.S.Neves and B.Opic. Optimal embeddings and Compact embeddings of Bessel-potential-type spaces, Pre-Publicacoes do Depurtmento de Matematica, Universidade de Coimbra, Preprint Number 06-39, (submitted)

49. A.Gogatishvili, L.Pick. Calderon-type theorems for operators of non-standard endpoint behavior   Preprint No. MATH-KMA-2007/251, 13 pages, (submitted)

50. A.Gogatishvili, L.Pick and J.Schneider. Interpolation characterization of the rearrangement-invariant hull of a Besov space, Preprint, Institute of Mathematics, AS CR, Prague, 2007-12-27, 19 pages, (submitted)

51. V.Burenkov, A.Gogatishvili, V.Guliyev and R.Mustafayev. Sufficient conditions for boundedness of the Riesz potential in local Morrey-type spaces, Preprint, Institute of Mathematics, AS CR, Prague, 2007-12-21, 14 pages.

52. A. Gogatishvili, A. Kufner And L.E. Persson. Some new scales of charachterization of Hardy's inequality. Preprint, Institute of Mathematics, AS CR, Prague, 2007-12-28, 9 pages, submitted

53. A.Gogatishvili, P. Koskela and N. Shanmugalinam. Interpolation properties of Besov spaces on metric spaces,

54. A. Gogatishvili, A. Kufner and L.E. Persson,An equivalence theorems with application to Hardy's inequality. Research Report 8, Department of Mathematics, Lule\aa \ University of Technology, 2007. 1-20.

Papers in conference proceedings

55. A. Gogatishvili. Fractional maximal functions with respect to the basis of theconvex comperable sets in weighted Lebesgue spaces (Russian).   In: the book of collected works Extremal problems, functional analyses and their applications, Moscow State University press 1988, pp.38-40.

56. A. Gogatishvili. Potentials in weighted Lorentz spaces for critical exponent (Russian). In: Reports of Enlarged Sessions of the Seminar of I. N. Vekua Institute   of Applied Mathematics vol. 3, no 2, Tbilisi University press 1988,   pp.25-28.

57. A. Gogatishvili. Riesz transforms and maximal functions in Morrey-Campanato type    spaces and in weighted Zygmund spaces. In: Reports of Enlarged   Session of the Seminar of I.N. Vekua institute of Applied mathematics,    vol. 5, no 2, Tbilisi University press 1990, pp. 41-43.

58. A. Gogatishvili. Riesz transforms in weighted $L\log L$ classes (Russian). In: Union School on Operator Theory in Function Spaces, Abstracts of Lectures, Ulyanovsk 5.-12.9. 1990, p. 68.

59. A. Gogatishvili. Weighted weak type inequalies for a strong maximal function. In:   Abstracts of Symposium on continuum mechanics and related problems analysis, Tbilisi, 1991, p.52.

60. A. Gogatishvili. General weak--type inequalities for the maximal operators defined in spaces of the homogeneous type. In: Reports of Enlarged    Sessions of the Seminar of I.N. Vekua Institute of Applied Mathematics, vol. 7, no. 2, Tbilisi University press 1992, pp. 14-16.

61. I. Genebashvili, A. Gogatishvili and V. Kokilashvili. Solutions of Some Weight Problems. Function spaces, differential operators and nonlinear analysis, (Frie-dri-chro-da, 1992), 264--273. Teubner--Texte Math., 133. Teubner, Stuttgart, 1993. (MR 95a:42028)

62. A. Gogatishvili and V. Kokilashvili.Criteria of weight inequalities for integral transforms defined on on homogeneous type spases.Topological vector spaces, algebras and related areas, (Hamilton, ON, 1994), 251-262. Pitman Res. Notes Math. ser., 316, Longman Sci. Tech., Harlow, 1994.   (MR 96a:42021)

63. A. Gogatishvili. Weighted inequalities for one-- sided maximal functions in Orlicz classes. Function spaces, differential operators and nonlinear analysis. Proceedings of the conference held in Paseky nad Jizerou, Czech Republic, September 3-9, 1995, Prague: Prometheus Publishing House, 201-205, 1996.

64. A. Gogatishvili. Discretization and anti-discretization of function spaces, In the proceedings of the The Autumn Conference Mathematical Society of Japan, September 25-28, 2002, Shimane University, Matsue, 63-72.

65. A.Gogatishvili, S.Moritoh, M.Niwa and T.Sobukawa.Interpolation theorems for block-Lorentz spaces. In the Proceedings of the International Symposium on Banach and Function Spaces, Kitakyushu, Japan, October 2-4, 2003, 215-223, Yokohama Publishers, 2004.

66.    A.Gogatishvili, J.S.Neves and B.Opic. Optimality of embeddings of Bessel-potential-type spaces, "Function spaces, differential operators and nonlinear analysis" Proceedings of the conference held in Milovy, Czech Republic, May 28- June2, 2004, Mathematical Institue of the Academy of Sciences of the Czech Republic, Praha, 97-112, 2005.