On a measure of non-compactness for singular integrals
type: Item
instance of: scholarly article
title: On a measure of non-compactness for singular integrals
zbMATH Open document ID: 1055.42009
DOI: 10.1155/2003/927590
author: Alexander Meskhi
published in: Journal of Function Spaces and Applications
publication date: 2004-10-28T00:00:00Z
review text: Summary: It is proved that there exists no weight pair \((v,w)\) for which a singular integral operator is compact from the weighted Lebesgue space \(L^p_w(R^n)\) to \(L^p_v(R^n)\). Moreover, a measure of non-compactness for this operator is estimated from below. Analogous problems for Cauchy singular integrals defined on Jordan smooth curves are studied.
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 2111352
zbMATH Keywords: measure of non-compactness
zbMATH Keywords: essential norm
zbMATH Keywords: singular integrals
zbMATH Keywords: Riesz transform
zbMATH Keywords: Hilbert transform
zbMATH Keywords: Cauchy integral
zbMATH Keywords: weights
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2003/927590
OpenAlex ID: W1988556891
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description: scientific article; zbMATH DE number 2111352