Boundedness of the anisotropic Riesz potential in anisotropic local Morrey-type spaces

被引：7

作者：

Akbulut, A. ^{[1
]}

Guliyev, V. S. ^{[1
,2
]}

Muradova, Sh. A. ^{[2
]}

机构：

[1] Ahi Evran Univ, Dept Math, TR-40200 Kirsehir, Turkey

[2] Inst Math & Mech, Dept Math Anal, AZ-1145 Baku, Azerbaijan

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2013年 / 58卷 / 02期

关键词：

anisotropic Riesz potential; anisotropic local and global Morrey-type spaces; Hardy operator on the cone of monotonic functions; Primary; 42B20; 42B25; 42B35; SUFFICIENT CONDITIONS; MAXIMAL OPERATOR; SINGULAR-INTEGRALS; EMBEDDINGS;

D O I：

10.1080/17476933.2011.575465

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The problem of boundedness of the anisotropic Riesz potential in local Morrey-type spaces is reduced to the problem of boundedness of the Hardy operator in weighted L p -spaces on the cone of non-negative non-increasing functions. This allows obtaining sharp sufficient conditions for boundedness for all admissible values of the parameters, which, for a certain range of the parameters wider than known before, coincide with the necessary ones.

引用

页码：259 / 280

页数：22

共 30 条

[1]

ADAMS DR, 1975, DUKE MATH J, V42, P765, DOI 10.1215/S0012-7094-75-04265-9

[2]

Akbulut A., BOUNDEDNESS AN UNPUB

[3]

[Anonymous], 1993, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals

[4]

BESOV OV, 1966, DOKL AKAD NAUK SSSR+, V169, P1250

[5]

Bramanti M, 1996, B UNIONE MAT ITAL, V10B, P843

[6]

Burenkov V., 2011, POTENTIAL ANAL, V35, P1

[7]

[Буренков B.И. Burenkov V.I.], 2006, [Доклады Академии наук, Doklady Akademii nauk], V409, P443

[8]

Burenkov VI, 2010, EURASIAN MATH J, V1, P32

[9] Boundedness of the fractional maximal operator in local Morrey-type spaces [J].

Burenkov, V. I. ;

Gogatishvili, A. ;

Guliyev, V. S. ;

Mustafayev, R. Ch. .

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS, 2010, 55 (8-10) :739-758

[10] Necessary and sufficient conditions for boundedness of the maximal operator in local Morrey-type spaces [J].

Burenkov, VI ;

Guliyev, HV .

STUDIA MATHEMATICA, 2004, 163 (02) :157-176

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