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AMIRAN
GOGATISHVILI
Research papers in academic
journals
2.
A.
Gogatishvili.
Fractional maximal functions with respect to the basis of the convex comparable
sets in weighted Lebesgue spaces.
(Russian. English
and Georgian Summaries) Soobshch. Akad.
Nauk Grusin.
SSR,
129(1988), no. 2, 273 - 275. MR0953054 (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. MR0953066 (89i:42033)
4.
A.
Gogatishvili. Riesz transforms and maximal
functions in '(L) classes.
(Russian and Georgian Summaries) Soobshch.
Akad. Nauk Grusin.
SSR, 137(1990), no. 3, 489 - 492. MR1087544 (91j:42009)
5.
A.
Gogatishvili, V.Kokilashvili and M.Krbec.
Maximal functions in the classes '(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. MR1094013 (92c:42018)
6.
A.
Gogatishvili. Maximal
functions with respect to the basis of the comparable convex sets in
weighted Lebesgue spaces. (Russian.
English Summary) Trudy Tbiliss. Mat. Inst.
Razmadze Akad.
Nauk Grusin.
SSR, 95(1990), 20- 38. MR1119755 (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. MR1221298 (94e:26037)
8.
A
Gogatishvili.
General weak type inequalities for maximal operators and singular
integrals.
(Georgian Summary) Proc. A.Razmadze Math.
Inst.,
101(1992), 47 - 63. MR1251273 (95e:42015)
9.
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.
MR1248367(94m:42040)
10.
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. MR1247940 (94m:42041)
11.
A.
Gogatishvili. Riesz transforms and maximal
functions
in '(L) classes. (Georgian Summary) Proc. A.Razmadze
Math. Inst., 102(1993), 59 - 70. MR1268817 (95d:42024)
12.
A.Gogatishvili.
Hilbert transform in Zygmund
classes. (Georgian Summary) Proc. A.Razmadze
Math.
Inst., 102(1993), 71 - 84. MR1268818 (95d:47065)
13.
A.Gogatishvili, V. Kokilashvili
and M. Krbec. Maximal functions, φ'(L)
classes
and Carleson measures. (Georgian Summary)
Proc. A.Razmadze Math. Inst., 102(1993),
85 - 97.MR1268819
(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.
MR1249621 (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. MR1251491 (94j:42030)
16.
A.
Gogatishvili, V. Kokilashvili. 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(1993), no. 6, 721 - 755;(English
Summary)
Georgian
Math.
J. 1(1994), no. 6, 641 - 673. MR1296573 (96b:42021)
17.
A.
Gogatishvili, V. Kokilashvili. Necessary
and
sufficient conditions for weighted Orlicz
class
inequalities for maximal functions and singular integrals. I (English
Summary)
Georgian Math. J. 2(1995), no. 4, 361 - 384. MR1344301 (96g:42010)
18.
A.
Gogatishvili, V. Kokilashvili. Necessary
and
sufficient conditions for weighted Orlicz
class
inequalities for maximal functions and singular integrals. II (English
Summary)
Georgian Math. J. 2(1995), no. 5, 445 - 468. MR1351334 (96m:42031)
19.
I. Genebashvili, A.
Gogatishvili and V. Kokilashvili.
Criteria of two-weighted inequalities for integral 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). MR1469056 (99c:42030)
20.
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.
MR1397815
(97k:42029)
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. MR1407384 (98m:42020)
22.
A.
Gogatishvili. Maximal functions and singular integrals on Lp,'
spaces. Proc. A.Razmadze Math. Inst.,
114(1997), 112 - 115. MR1638706 (99i:46017)
23.
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. MR1468961 (98m:42021)
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. MR1733113 (2001f:47085)
25.
A.
Gogatishvili. Fractional maximal functions in weighted Banach
function spaces, Real Analysis and Exchange, 25(1999/2000), no.1, 291 -
316.
MR1758007 (2001g:42029)
26.
A.Gogatishvili and L.Pick.
Duality principles and reduction theorems, Math. Inequal.
Appl.,
3(2000),
no.
4, 539 - 558. MR1786395 (2002c:46056)
27.
A.Gogatishvili and T.Sobukawa. On
the extrapolation estimates, Math. Inequal.
Appl.,
6(2003),
no.
1, 97 - 104. MR1950654 (2003k:46030).
28.
A.Gogatishvili and L.Pick. Discretization
and antidiscretization
of rearrangement–invariant norms. Publ. Mat., 47(2003), no. 2, 311 -
358.
MR2006487 (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. MR2083821 (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. MR2107486 (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.
MR2111802
(2005k:46048)
32.
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.
MR2177070 (2006f:26002)
33.
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.
MR2182593 (2006g:46051)
34.
A. Gogatishvili
and P. Koskela. A non-doubling Trudinger
inequality, Studia Math. 170 (2005), no.
2, 113 -
119. MR2184101 (2007b:26041)
35.
A. Gogatishvili
and L. Pick. Embeddings and duality theorems for weak classical Lorentz
spaces,
Canad. Math. Bull. 49(2006), no. 1, 82 -
95.
MR2198721 (2006k:26024)
36.
A.
Gogatishvili, A. Kufner, L.-E. Persson
and A. Wedestig. Compactness of the Hardy
operator
and its limiting case.
37.
A.
Gogatishvili, B. Opic and L. Pick.
Weighted
inequalities for Hardy-type operators involving suprema,
Collect.Math. 57(2006), no.3, 227 - 255.
MR2264321
(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 (2008f:46044)
40.
A.
Gogatishvili, M. Johansson, C. A. Okpoti
and L.-E. Persson. Characterization of
embeddings in Lorentz spaces,
Bull. Austral. Math. Soc. 76 (2007), no. 1, 69 - 92. MR2343440
(2008j:46017)
41.
A. Gogatishvili
and L. Pick. A reduction theorem for supremum
operators, J. Comput. Appl. Math.
208(2007), no.1,
270 - 279. MR2347749 (2009a:26013)
42.
A.Gogatishvili and V.I.Ovchinnikov.
Interpolation orbits and optimal Sobolev’s
embeddings, J. Funct. Anal. 253(2007) no.
1, 1 - 17.
MR2362416 (2008k:46096)
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 (2008m:26029)
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 and 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 (2010c:46079)
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 (2010c:46074)
48.
A.
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 (2010b:42021)
49.
A.Gogatishvili and L.Pick.
Calderon-type theorems for operators of non-standard endpoint behavior.
50.
A.Gogatishvili, P. Koskela and N.
Shanmugalinam. Interpolation properties of Besov spaces on metric spaces. Math. Nachr.
283(2010), no. 2, 215 - 231. MR2604119
51.
A.Gogatishvili, J.Neves and B.Opic.
Optimal embeddings of Bessel-potential-type spaces into
generalized Holder spaces involving k-modulus of smoothness, Potential
Anal.
32(2010),no 3, 201 - 228. MR2595366
52.
A.
Gogatishvili,
A. Kufner and L.E. Persson.
Some
new scales of characterization of Hardy’s inequality. Proc. Est.Acad. Sci. 59(2010), no. 1, 7
-
18. MR2647852
53.
A.
Gogatishvili, J.Neves and B.Opic.
Sharp estimates of the k-modulus of smoothness of Bessel potentials, J. London Math.
Soc. 81(2010), no.3, 608
-
624.
MR2650787
54.
V. Burenkov, A.
Gogatishvili, V. Guliyev and R. Mustafayev.
Boundedness of the fractional maximal
operator in
local Morrey-type spaces. Complex Var.
Elliptic Equ.,
55(2010), no. 8-10, 739 – 758. MR2674862
55.
A.Gogatishvili, J.Neves
and B.Opic.
Compact embeddings of Bessel-potential-type spaces
into generalized Hölder spaces involving
k-modulus
of smoothness, Z. Anal. Anwend. 30(2011), no 1, 2011, 1–27.
Papers
accepted for publication
56.
A.
Gogatishvili and R.Mustafayev.
Equivalence of norms of Riesz potential
and
fractional maximal function in generalized Morrey
spaces. Preprint 135, Institute of
57.
V.Burenkov, A.Gogatishvili,
V.Guliyev and R.Mustafayev.
Sufficient
conditions
for
boundedness of the Riesz
potential in local Morrey-type
spaces, Preprint 85,
58.
A.Caetano, A. Gogatishvili and B. Opic.
Compact
embeddings
of
Besov spaces involving only
slowly varying
smoothness, Preprint 188,
59.
A.Gogatishvili and R. Mustafayev.
The
multidimensional
reverse
Hardy inequalities. Preprint 179, Institute of
60.
A.Gogatishvili and R. Mustafayev.
Dual
spaces
of
local Morrey-type spaces.
Preprint 137,
Institute of
Preprints
and
Papers
submitted
for publication
61.
A.Gogatishvili, L.Pick and J.Schneider .
Interpolation characterization of the rearrangement-invariant hull of a
Besov space, Preprint No. MATH-KMA-2008/269
pp. 17.
62.
A.Caetano, A.
Gogatishvili and B. Opic.
Sharp embeddings of Besov spaces involving
only
slowly varying smoothness, Preprint, Univ. Aveiro,
2008,
pp.
34.
Preprint 178, Institute of
63.
L.Bernardis, A.
Gogatishvili, F.-J.Martın-Reyes,
P. Ortega
Papers
in conference proceedings
64.
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,
65.
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.
66.
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
67.
A.
Gogatishvili. Riesz transforms in weighted
$L\log L$
classes (Russian). In:
68.
A.
Gogatishvili. Weighted weak type inequalies
for a
strong maximal function. In: Abstracts of Symposium on
continuum
mechanics and related problems analysis,
69.
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,
70.
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,
71.
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)
72.
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
73.
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,
74.
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.
75.
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 Institute 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,
Differential
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.
77.
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.
