Algebras of singular integral operators on rearrangement-invariant spaces and Nikolski ideals
type: Item
instance of: scholarly article
title: Algebras of singular integral operators on rearrangement-invariant spaces and Nikolski ideals
zbMATH Open document ID: 1022.47017
author: Oleksiy Karlovych
published in: The New York Journal of Mathematics
publication date: 2003-04-07T00:00:00Z
full work available at URL: https://eudml.org/doc/122943
full work available at URL: 8-14nf.htm
review text: Let \(\mathbb{T}\) be the unit circle and \(X({\mathbb{T}}, |d\tau|/2\pi)\) be a reflexive rearrangement-invariant space with nontrivial Boyd indices. It is considered the algebra \(\text{Alg} (\Omega, S)\) generated by the Cauchy singular integral operator \(S\) and the operator \(M_\varphi\) of multiplication by the function \(\varphi \in \Omega \subset L^\infty\). The author constructs a pre-symbol of the operators from \(\text{Alg} (\Omega, S)\) and gives necessary conditions for Fredholmness. Contents: 1. Introduction. 2. Rearrangement-invariant spaces and their indices. 3. Nikolski ideals associated with Douglas algebras. 4. The pre-symbol of the algebra \(\text{Alg} (\Omega, S)\). References.
reviewed by: N. Karapetiants
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 47A53
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 1893532
zbMATH Keywords: Douglas algebra
zbMATH Keywords: singular integral operators
zbMATH Keywords: rearrangement-invariant spaces
zbMATH Keywords: Nikolski ideals
zbMATH Keywords: Fredholmness
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1893532