Grand Lebesgue Spaces with Mixed Local and Global Aggrandization and the Maximal and Singular Operators

H. Rafeiro, S. Samko, S. Umarkhadzhiev

Research output: Contribution to journalArticlepeer-review

Abstract

The approach to “locally” aggrandize Lebesgue spaces, previously suggested by the authors and based on the notion of “aggrandizer”, is combined with the usual “global” aggrandization. We study properties of such spaces including embeddings, dependence of the choice of the aggrandizer and, in particular, we discuss the question when these spaces are not new, coinciding with globally aggrandized spaces, and when they proved to be new. We study the boundedness of the maximal, singular, and maximal singular operators in the introduced spaces.

Original languageEnglish
Pages (from-to)1087-1106
Number of pages20
JournalAnalysis Mathematica
Volume49
Issue number4
DOIs
Publication statusPublished - Dec 2023

Keywords

  • grand Lebesgue space
  • maximal function
  • maximal singular integral
  • singular integral

ASJC Scopus subject areas

  • Analysis
  • General Mathematics

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