Weighted riesz bounded variation spaces and the nemytskii operator

David Cruz-Uribe, Oscar M. Guzmán, Humberto Rafeiro

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We define a weighted version of the Riesz bounded variation space. We show that a generalization of the Riesz theorem relating these spaces to the Sobolev space W1,ppIq holds for weighted Riesz bounded variation spaces when the weight belongs to the Muckenhoupt class. As an application, for weights belonging to the Muckenhoupt class, we characterize the globally Lipschitz Nemytskii operators acting in the weighted Riesz bounded variation spaces.

Original languageEnglish
Pages (from-to)125-139
Number of pages15
JournalAzerbaijan Journal of Mathematics
Volume10
Issue number2
Publication statusPublished - 2020

Keywords

  • A weights
  • Banach function spaces
  • Nemytskii operators
  • Riesz bounded variation spaces
  • Variable Lebesgue spaces

ASJC Scopus subject areas

  • General Mathematics

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