Coincidence of Variable Exponent Herz Spaces with Variable Exponent Morrey Type Spaces and Boundedness of Sublinear Operators in these Spaces

Humberto Rafeiro; Stefan Samko

doi:10.1007/s11118-020-09891-z

Coincidence of Variable Exponent Herz Spaces with Variable Exponent Morrey Type Spaces and Boundedness of Sublinear Operators in these Spaces

Humberto Rafeiro, Stefan Samko

Department of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

We introduce generalized local and global Herz spaces where all their characteristics are variable. As one of the main results we show that variable Morrey type spaces and complementary variable Morrey type spaces are included into the scale of these generalized variable Herz spaces. We also prove the boundedness of a class of sublinear operators in generalized variable Herz spaces with application to variable Morrey type spaces and their complementary spaces, based on the mentioned inclusion.

Original language	English
Pages (from-to)	437-457
Number of pages	21
Journal	Potential Analysis
Volume	56
Issue number	3
DOIs	https://doi.org/10.1007/s11118-020-09891-z
Publication status	Published - Mar 2022

Keywords

Function spaces
Herz spaces
Maximal function
Morrey spaces -and variable exponent spaces
Singular operators
Sublinear operators

ASJC Scopus subject areas

Analysis

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10.1007/s11118-020-09891-z

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title = "Coincidence of Variable Exponent Herz Spaces with Variable Exponent Morrey Type Spaces and Boundedness of Sublinear Operators in these Spaces",

abstract = "We introduce generalized local and global Herz spaces where all their characteristics are variable. As one of the main results we show that variable Morrey type spaces and complementary variable Morrey type spaces are included into the scale of these generalized variable Herz spaces. We also prove the boundedness of a class of sublinear operators in generalized variable Herz spaces with application to variable Morrey type spaces and their complementary spaces, based on the mentioned inclusion.",

keywords = "Function spaces, Herz spaces, Maximal function, Morrey spaces -and variable exponent spaces, Singular operators, Sublinear operators",

author = "Humberto Rafeiro and Stefan Samko",

note = "Funding Information: The research of H. Rafeiro was supported by a Research Start-up Grant of United Arab Emirates University, Al Ain, United Arab Emirates via Grant No. G00002994. The research of S. Samko was supported by: (a) Russian Foundation for Basic Research under the grant №19-01-00223, and (b) TUBITAK and Russian Foundation for Basic research under the grant №20-51-46003. Acknowledgments Publisher Copyright: {\textcopyright} 2021, Springer Nature B.V.",

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doi = "10.1007/s11118-020-09891-z",

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AU - Rafeiro, Humberto

AU - Samko, Stefan

N1 - Funding Information: The research of H. Rafeiro was supported by a Research Start-up Grant of United Arab Emirates University, Al Ain, United Arab Emirates via Grant No. G00002994. The research of S. Samko was supported by: (a) Russian Foundation for Basic Research under the grant №19-01-00223, and (b) TUBITAK and Russian Foundation for Basic research under the grant №20-51-46003. Acknowledgments Publisher Copyright: © 2021, Springer Nature B.V.

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N2 - We introduce generalized local and global Herz spaces where all their characteristics are variable. As one of the main results we show that variable Morrey type spaces and complementary variable Morrey type spaces are included into the scale of these generalized variable Herz spaces. We also prove the boundedness of a class of sublinear operators in generalized variable Herz spaces with application to variable Morrey type spaces and their complementary spaces, based on the mentioned inclusion.

AB - We introduce generalized local and global Herz spaces where all their characteristics are variable. As one of the main results we show that variable Morrey type spaces and complementary variable Morrey type spaces are included into the scale of these generalized variable Herz spaces. We also prove the boundedness of a class of sublinear operators in generalized variable Herz spaces with application to variable Morrey type spaces and their complementary spaces, based on the mentioned inclusion.

KW - Function spaces

KW - Herz spaces

KW - Maximal function

KW - Morrey spaces -and variable exponent spaces

KW - Singular operators

KW - Sublinear operators

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Coincidence of Variable Exponent Herz Spaces with Variable Exponent Morrey Type Spaces and Boundedness of Sublinear Operators in these Spaces

Abstract

Keywords

ASJC Scopus subject areas

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