A note on boundedness of operators in grand grand morrey spaces

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26 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 languageEnglish
Pages (from-to)349-356
Number of pages8
JournalOperator Theory: Advances and Applications
Volume229
DOIs
Publication statusPublished - 2013
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Analysis

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