Criteria for n(d)-normality of weighted singular integral operators with shifts and slowly oscillating data

Alexey Yu Karloviych, Yuri I. Karlovich, Amarino B. Lebre

Research output: Contribution to journalArticle

1 Citation (Scopus)

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+), 1 < p 1 < ∞, given by (Formula presented.). We prove criteria for the n-normality and d-normality on the space Lp(R+) of singular integral operators of the form A+P+γ + A−Pγ, where (Formula presented.) are operators in the Wiener algebras of functional operators with shifts and the operators (Formula presented.) are associated to the weighted Cauchy singular integral operator (Formula presented.) where γ ∈ C satisfies the condition 0 < 1/p + γ < 1. We assume that the coefficients ak, bk for k ∈ Z and the derivatives of the shifts α',β' are bounded continuous functions on R+ which may have slowly oscillating discontinuities at 0 and ∞.

Original languageEnglish
Pages (from-to)997-1027
Number of pages31
JournalProceedings of the London Mathematical Society
Volume116
Issue number4
DOIs
Publication statusPublished - 1 Apr 2018

Keywords

  • 45E05
  • 47A53
  • 47B33
  • 47B35
  • 47G10 (primary)
  • 47G30 (secondary)

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