On a Weighted Singular Integral Operator with Shifts and Slowly Oscillating Data

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

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

Let be orientation-preserving diffeomorphism (shifts) of onto itself with the only fixed points and and be the isometric shift operators on given by , , and where then the operator is Fredholm on and its index is equal to zero. Moreover, its regularizers are described. the weighted Cauchy singular integral operator. We prove that if a , a and c, d are continuous on R + and slowly oscillating at 0 and8, and then the operator (I -cUa) P+ 2 +(I -dUa) P-2 is Fredholm on L p(R +) and its index is equal to zero. Moreover, its regularizers are described.

Original languageEnglish
Pages (from-to)1101-1131
Number of pages31
JournalComplex Analysis And Operator Theory
Volume10
Issue number6
DOIs
Publication statusPublished - Aug 2016

Keywords

  • Orientation-preserving shift
  • Weighted Cauchy singular integral operator
  • Slowly oscillating function
  • Fredholmness
  • Index
  • FREDHOLMNESS
  • ALGEBRA

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