The singular integral operator and its commutator on weighted Morrey spaces

Shohei Nakamura; Yoshihiro Sawano

doi:10.1007/s13348-017-0193-7

The singular integral operator and its commutator on weighted Morrey spaces

Shohei Nakamura^*
, Yoshihiro Sawano

^*Corresponding author for this work

Mathematics

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

Abstract

In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey spaces; the A_q-theory by Muckenhoupt and Wheeden does not suffice. We also discuss the boundedness of the commutators. The difference between the maximal operator and the singular integral operators will be clarified. Further, the property of the sharp maximal operator is investigated.

Original language	English
Pages (from-to)	145-174
Number of pages	30
Journal	Collectanea mathematica
Volume	68
Issue number	2
DOIs	https://doi.org/10.1007/s13348-017-0193-7
Publication status	Published - 1 May 2017

Bibliographical note

Publisher Copyright:
© 2017, Universitat de Barcelona.

Keywords

Commutator
Local sharp maximal operator
Singular integral operators
Weighted morrey spaces

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1007/s13348-017-0193-7

Cite this

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abstract = "In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey spaces; the Aq-theory by Muckenhoupt and Wheeden does not suffice. We also discuss the boundedness of the commutators. The difference between the maximal operator and the singular integral operators will be clarified. Further, the property of the sharp maximal operator is investigated.",

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AU - Sawano, Yoshihiro

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N2 - In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey spaces; the Aq-theory by Muckenhoupt and Wheeden does not suffice. We also discuss the boundedness of the commutators. The difference between the maximal operator and the singular integral operators will be clarified. Further, the property of the sharp maximal operator is investigated.

AB - In this paper, we give necessary conditions and sufficient conditions respectively for the boundedness of the singular integral operator on the weighted Morrey spaces. We observe the phenomenon unique to the case of Morrey spaces; the Aq-theory by Muckenhoupt and Wheeden does not suffice. We also discuss the boundedness of the commutators. The difference between the maximal operator and the singular integral operators will be clarified. Further, the property of the sharp maximal operator is investigated.

KW - Commutator

KW - Local sharp maximal operator

KW - Singular integral operators

KW - Weighted morrey spaces

UR - https://www.scopus.com/pages/publications/85017214379

U2 - 10.1007/s13348-017-0193-7

DO - 10.1007/s13348-017-0193-7

M3 - Article

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JO - Collectanea mathematica

JF - Collectanea mathematica

IS - 2

ER -

The singular integral operator and its commutator on weighted Morrey spaces

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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