Definability of singular integral operators on Morrey-Banach spaces

被引：26

作者：

Ho, Kwok-Pun ^{[1
]}

机构：

[1] Educ Univ Hong Kong, Dept Math & Informat Technol, 10 Ping Rd, Hong Kong, Peoples R China

来源：

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN | 2020年 / 72卷 / 01期

关键词：

singular integral operator; Morrey space; Banach function space; variable exponent analysis; RIESZ-POTENTIALS; SOBOLEV EMBEDDINGS; VARIABLE EXPONENT; MAXIMAL OPERATOR; HARDY-SPACES; BOUNDEDNESS; COMMUTATORS; KERNELS;

D O I：

10.2969/jmsj/81208120

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give a definition of singular integral operators on Morrey- Banach spaces which include Orlicz-Morrey spaces and Morrey spaces with variable exponents. The main result of this paper ensures that the singular integral operator is well-defined on the Morrey-Banach spaces. Therefore, it provides a solid foundation for the study of singular integral operators on Morrey type spaces. As an application of our main result, we study commutators of singular integral operators on Morrey-Banach spaces.

引用

页码：155 / 170

页数：16

共 35 条

[21] VECTOR-VALUED SINGULAR INTEGRAL OPERATORS ON MORREY TYPE SPACES AND VARIABLE TRIEBEL-LIZORKIN-MORREY SPACES [J].

Ho, Kwok-Pun .

ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2012, 37 (02) :375-406

[22]

Ho KP, 2012, ANAL MATH, V38, P173, DOI 10.1007/s10476-012-0302-5

[23]

Kokilashvili V, 2008, ARMEN J MATH, V1, P18

[24]

Lu S., 1998, HOKKAIDO MATH J, V27, P219, DOI DOI 10.14492/H0KMJ/1351001259.MR1608644

[25] Sobolev embeddings for Riesz potentials of functions in Morrey spaces of variable exponent [J].

Mizuta, Yoshihiro ;

Shimomura, Tetsu .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2008, 60 (02) :583-602

[26] CONTINUITY PROPERTIES FOR RIESZ POTENTIALS OF FUNCTIONS IN MORREY SPACES OF VARIABLE EXPONENT [J].

Mizuta, Yoshihiro ;

Shimomura, Tetsu .

MATHEMATICAL INEQUALITIES & APPLICATIONS, 2010, 13 (01) :99-122

[27] Boundedness of fractional integral operators on Morrey spaces and Sobolev embeddings for generalized Riesz potentials [J].

Mizuta, Yoshihiro ;

Nakai, Eiichi ;

Ohno, Takao ;

Shimomura, Tetsu .

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, 2010, 62 (03) :707-744

[28] On the solutions of quasi-linear elliptic partial differential equations [J].

Morrey, Charles B., Jr. .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1938, 43 (1-3) :126-166

[29] HARDY-LITTLEWOOD MAXIMAL OPERATOR, SINGULAR INTEGRAL-OPERATORS AND THE RIESZ-POTENTIALS ON GENERALIZED MORREY SPACES [J].

NAKAI, E .

MATHEMATISCHE NACHRICHTEN, 1994, 166 :95-103

[30] Orlicz-Morrey spaces and the Hardy-Littlewood maximal function [J].

Nakai, Eiichi .

STUDIA MATHEMATICA, 2008, 188 (03) :193-221

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