Semi-Fredholmness of Weighted Singular Integral Operators with Shifts and Slowly Oscillating Data

Alexei Yu Karlovich, Yuri I. Karlovich, Amarino B. Lebre

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

Let α, β be orientation-preserving homeomorphisms of [0,∞] onto itself, which have only two fixed points at 0 and ∞, and whose restrictions to ℝ+ = (0,∞) are diffeomorphisms, and let Uα, Uβ be the corresponding isometric shift operators on the space Lp(ℝ+) given by (Formula presented) for (Formula presented). We prove sufficient conditions for the right and left Fredholmness on Lp(ℝ+) of singular integral operators of the form (Formula presented), where (Formula presented) is a weighted Cauchy singular integral operator, (Formula presented) and (Formula presented) are operators in the Wiener algebras of functional operators with shifts. We assume that the coefficients ak, bk for (Formula presented) and the derivatives of the shifts (Formula presented) are bounded continuous functions on ℝ+ which may have slowly oscillating discontinuities at 0 and ∞.

Original languageEnglish
Title of host publicationOperator Theory
Subtitle of host publicationAdvances and Applications
PublisherSpringer International Publishing
Pages221-246
Number of pages26
Volume267
DOIs
Publication statusPublished - 2018

Publication series

NameOperator Theory: Advances and Applications
Volume267
ISSN (Print)0255-0156
ISSN (Electronic)2296-4878

Keywords

  • Left Fredholmness
  • Mellin pseudodifferential operator
  • Right Fredholmness
  • Slowly oscillating shift
  • Weighted singular integral operator
  • Wiener algebra of functional operators

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