Riesz type potential operators in generalized grand Morrey spaces

Vakhtang Kokilashvili, Alexander Meskhi, Humberto Rafeiro

Research output: Contribution to journalArticlepeer-review

20 Citations (Scopus)

Abstract

We introduce generalized grand Morrey spaces in the framework of quasimetric measure spaces, in the spirit of the so-called grand Lebesgue spaces. We prove a kind of reduction lemma which is applicable to a variety of operators to reduce their boundedness in generalized 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 as well as the boundedness of Calderón-Zygmund operators. The boundedness of Riesz type potential operators is also obtained in the framework of homogeneous and also in the nonhomogeneous cases in generalized grand Morrey spaces.

Original languageEnglish
Pages (from-to)43-64
Number of pages22
JournalGeorgian Mathematical Journal
Volume20
Issue number1
DOIs
Publication statusPublished - Mar 1 2013
Externally publishedYes

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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