A note on boundedness of operators in grand grand morrey spaces

Humberto Rafeiro

doi:10.1007/978-3-0348-0516-2_19

A note on boundedness of operators in grand grand morrey spaces

Humberto Rafeiro

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

34 Citations (Scopus)

Abstract

In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces.We prove a kind of reduction lemma which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder´on-Zygmund operators in the framework of grand grand Morrey spaces.

Original language	English
Pages (from-to)	349-356
Number of pages	8
Journal	Operator Theory: Advances and Applications
Volume	229
DOIs	https://doi.org/10.1007/978-3-0348-0516-2_19
Publication status	Published - 2013
Externally published	Yes

Keywords

Calderón-Zygmund operator
Hardy-Littlewood maximal operator
Maximal operator
Morrey spaces

ASJC Scopus subject areas

Analysis

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10.1007/978-3-0348-0516-2_19

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title = "A note on boundedness of operators in grand grand morrey spaces",

abstract = "In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces.We prove a kind of reduction lemma which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder´on-Zygmund operators in the framework of grand grand Morrey spaces.",

keywords = "Calder{\'o}n-Zygmund operator, Hardy-Littlewood maximal operator, Maximal operator, Morrey spaces",

author = "Humberto Rafeiro",

note = "Funding Information: H.R. was supported in part by Funda¸c{\^a}o para a Ci{\^e}ncia e a Tecnologia (FCT), Grant SFRH/ Publisher Copyright: {\textcopyright} 2013 Springer Basel.",

year = "2013",

doi = "10.1007/978-3-0348-0516-2_19",

language = "English",

volume = "229",

pages = "349--356",

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T1 - A note on boundedness of operators in grand grand morrey spaces

AU - Rafeiro, Humberto

PY - 2013

Y1 - 2013

N2 - In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces.We prove a kind of reduction lemma which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder´on-Zygmund operators in the framework of grand grand Morrey spaces.

AB - In this note we introduce grand grand Morrey spaces, in the spirit of the grand Lebesgue spaces.We prove a kind of reduction lemma which is applicable to a variety of operators to reduce their boundedness in grand grand Morrey spaces to the corresponding boundedness in Morrey spaces. As a result of this application, we obtain the boundedness of the Hardy-Littlewood maximal operator and Calder´on-Zygmund operators in the framework of grand grand Morrey spaces.

KW - Calderón-Zygmund operator

KW - Hardy-Littlewood maximal operator

KW - Maximal operator

KW - Morrey spaces

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EP - 356

JO - Operator Theory: Advances and Applications

JF - Operator Theory: Advances and Applications

ER -

A note on boundedness of operators in grand grand morrey spaces

Abstract

Keywords

ASJC Scopus subject areas

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