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,
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.
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.
20.
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.
(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, Real Anal. Exchange,
33(2007/2008), no. 1, 249-258. MR2402877 (2009b:26030)
45. M. Carro, A. Gogatishvili,
J. Martin, L. Pick. Weighted inequalities involving two Hardy
operators with applications to embeddings of function spaces, J. operator
Theory 59(2008), no. 2, 309-332. MR2411048 (2009f:26024)
46.A.M.Caetano, A.Gogatishvili
and B.Opic. Sharp embeddings of Besov
spaces involving only logarithmic smoothness, J.
Approx. Theory 152(2008), no. 2, 188-214. MR2422148
47. A.Gogatishvili,
J.S.Neves and B.Opic. Optimal embeddings and Compact
embeddings of Bessel-potential-type spaces, Math.
Zeitshrift,
262(2009), no. 3, 645--682. MR2506313
48. Gogatishvili,
A. Kufner and L.E. Persson. Some new scales of weight characterizations of the
class Bp, Acta
Math. Hungar.123(2009), no.4, 365--377. MR2506756
49. A.Gogatishvili,
L.Pick. Calderon-type theorems for operators of
non-standard endpoint behavior.
Papers
accepted for publication
50. A. Gogatishvili, A.
Kufner And L.E. Persson. Some new scales of charachterization of Hardy's inequality. Proceedings
of the Estonian Academy of Sciences 58(2009), no. 4, Preprint 103, Institute of
Mathematics AS CR, Prague 2007, pp. 9.
51 A.Gogatishvili,
P. Koskela and N. Shanmugalinam.
Interpolation properties of Besov
spaces on metric spaces. Preprint 151, Institute of
52. A.Gogatishvili,
J.Neves and B.Opic.
Optimal embeddings of Bessel-potential-type spaces into generalized Holder
spaces involving k-modulus of smoothness, Preprint, Univ. Coi\-mbra,
2008, pp. 24. Preprint 182, Institute of
53. A Gogatishvili, J.Neves and B.Opic. Sharp estimates of the
k-modulus of smoothness of Bessel potentials, Preprint, Univ. Coimbra, 2008,
pp. 17. Preprint 177, Institute of
Preprints and Papers submitted
for publication
54. 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.
55. A.Gogatishvili, L.Pick and J.Schneider
.Interpolation characterization of the rearra\-nge\-ment\--invariant
hull of a Besov space, Preprint No. MATH-KMA-2008/269 pp. 17.
56 A. Gogatishvili and R.Mustafayev. Equivalence of norms of Riesz potential and fractional maximal function in Morrey-type spaces. Preprint 135, Institute of
57. V.Burenkov, A.Gogatishvili, V.Guliyev and R.Mustafayev. Boundedness of
the fractional maximal operator in local Morrey-type
spaces. Preprint 136, Institute of
59. A.Gogatishvili
and R. Mustafayev. Dual spaces of local
Morrey-type spaces. Preprint 137, Institute of
60. A.Caetano,
A. Gogatishvili and B. Opic. Sharp embeddings of Besov spaces involving only slowly varying smoo\-thness, Preprint, Univ. Aveiro,
2008, pp. 34. Preprint 178, Institute of
61. A.Gogatishvili
and R. Mustafayev. The multidimensional reverse Hardy
inequalities. Preprint 179, Institute of
62. A.Caetano,
A. Gogatishvili and B. Opic. Compact embeddings of Besov spaces involving only slowly varying smoothness,
Preprint 188,
62. A.Gogatishvili,
J.Neves and B.Opic.
Compact embeddings of Bessel-potential-type spaces into generalized Holder
spaces involving k-modulus of smoothness, Preprint 189,
Papers
in conference proceedings
63. 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,
64. 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.
65. 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
66. A. Gogatishvili. Riesz transforms
in weighted $L\log L$ classes (Russian). In:
67. A. Gogatishvili. Weighted weak
type inequalies for a strong maximal function.
In: Abstracts of Symposium on continuum mechanics and related
problems analysis,
68. 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,
69.
70. 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)
71. 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
72. 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,
73. 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.
74. 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.
76. A. Gogatishvili,
A. Kufner and L.E. Persson An equivalence theorems with application to
Hardy's inequality. In the book ``Function Spaces, Differencial
Operators, General Topology, Problems of Mathematical Educations'',
Proceedings of the 3th International Conference
dedicated to Lev Dmitrievich Kudryavtsev
on the occasion of his eighty-fifth birthday, 278-298. M. 2008.
76. W. D. Evans, A. Gogatishvili and B. Opic The ρ-quasiconcave
functions and weighted inequalities, Inequalities and Applications, Conference
on Inequalities and Applications, Noszvaj (Hungary),
September 2007.International Series of Numerical Mathematics, 157, Bandle, C., Gilányi, A., Losonczi, L., Páles, Z. and Plum,
M.(eds.), Birkhâuser Verlag,
Basel, 2009. 121--132.
