The cauchy singular integral operator on weighted variable lebesgue spaces

Alexei Yu Karlovich, Ilya M. Spitkovsky

Research output: Contribution to journalArticlepeer-review

Abstract

Let p : ℝ → (1,∞) be a globally log-Hölder continuous variable exponent and w : ℝ → [0,∞] be a weight. We prove that the Cauchy singular integral operator S is bounded on the weighted variable Lebesgue space Lp(⋅)(ℝ,w) = {f : fw ∈ Lp(⋅)(ℝ)} if and only if the weight w satisfies (Formula Presented).

Original languageEnglish (US)
Pages (from-to)275-291
Number of pages17
JournalOperator Theory: Advances and Applications
Volume236
DOIs
StatePublished - 2014

Keywords

  • Cauchy singular integral operator
  • Hardy-littlewood maximal operator
  • Log-Hölder continuous variable exponent
  • Weighted variable lebesgue space

ASJC Scopus subject areas

  • Analysis

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