A characterization of weighted Sobolev spaces via weighted Riesz bounded variation spaces

David Cruz-Uribe, Oscar Guzmán, Humberto Rafeiro

Research output: Contribution to journalArticlepeer-review

Abstract

We introduce weighted Riesz bounded variation spaces defined on an open subset of n-dimensional Euclidean space and use them to characterize weighted Sobolev spaces when the weight belongs to the Muckenhoupt class. As an application, using Rubio de Francia’s extrapolation theory, we obtain a similar characterization of variable exponent Sobolev spaces via variable exponent Riesz bounded variation spaces.

Original languageEnglish
Pages (from-to)287-304
Number of pages18
JournalStudia Mathematica
Volume274
Issue number3
DOIs
Publication statusPublished - 2024

Keywords

  • Muckenhoupt Ap weights
  • Riesz bounded variation spaces
  • Rubio de Francia extrapolation
  • Sobolev spaces
  • variable Lebesgue spaces

ASJC Scopus subject areas

  • General Mathematics

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