On singular integral operators with semi-almost periodic coefficients on variable Lebesgue spaces

Alexei Yu Karlovich, Ilya M. Spitkovsky

Research output: Contribution to journalArticle

Abstract

Let a be a semi-almost periodic matrix function with the almost periodic representatives al and ar at -∞ and +∞, respectively. Suppose p:R→(1,∞) is a slowly oscillating exponent such that the Cauchy singular integral operator S is bounded on the variable Lebesgue space Lp(.)(R). We prove that if the operator aP+Q with P=(I+S)/2 and Q=(I-S)/2 is Fredholm on the variable Lebesgue space LNp(.)(R), then the operators alP+Q and arP+Q are invertible on standard Lebesgue spaces LNql(R) and LNqr(R) with some exponents ql and qr lying in the segments between the lower and the upper limits of p at -∞ and +∞, respectively.

Original languageEnglish (US)
Pages (from-to)706-725
Number of pages20
JournalJournal of Mathematical Analysis and Applications
Volume384
Issue number2
DOIs
StatePublished - Dec 15 2011

Keywords

  • Almost-periodic function
  • Fredholmness
  • Invertibility
  • Semi-almost periodic function
  • Singular integral operator
  • Slowly oscillating function
  • Variable Lebesgue space

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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