Pseudodifferential operators approach to singular integral operators in weighted variable exponent Lebesgue spaces on Carleson curves
type: Item
instance of: scholarly article
title: Pseudodifferential operators approach to singular integral operators in weighted variable exponent Lebesgue spaces on Carleson curves
zbMATH Open document ID: 1231.47049
published in: Integral Equations and Operator Theory
publication date: 2011-05-20T00:00:00Z
review text: The paper presents general results concerning one-dimensional singular integral operators, i.e., operators with Cauchy kernel, on Carleson curves \(\Gamma\). The functional frame is given by Lebesgue spaces \(L^{p(\cdot)}(\Gamma, w)\) with variable exponent \(p= p(x)\), \(x\in\Gamma\), and weights \(w\) having a finite set of oscillation singularities. The authors adopt the modern techniques for pseudodifferential and Mellin type operators, and obtain precise criteria for Fredholmness. An important tool in the proofs is represented by the local principle of \textit{I. B. Simonenko} [Izv. Akad. Nauk SSSR, Ser. Mat. 29, 567--586, 757--782 (1965; Zbl 0146.13101)].
reviewed by: Luigi Rodino
Mathematics Subject Classification ID: 47G30
Mathematics Subject Classification ID: 35S05
zbMATH DE Number: 5898353
zbMATH Keywords: Cauchy singular integral operators
zbMATH Keywords: pseudodifferential operators
zbMATH Keywords: Mellin operators
author: Vladimir Rabinovich
author: S. G. Samko
MaRDI profile type: Publication
full work available at URL: s00020-010-1848-x
OpenAlex ID: W2075247676
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DOI: 10.1007/S00020-010-1848-X
description: scientific article; zbMATH DE number 5898353