Singular integral operators with non-necessarily bounded kernels on spaces of homogeneous type
type: Item
instance of: scholarly article
title: Singular integral operators with non-necessarily bounded kernels on spaces of homogeneous type
zbMATH Open document ID: 0795.42010
DOI: 10.1016/0001-8708(92)90024-F
author: Roberto A. Macías
author: Carlos Segovia
author: José Luis Torrea
published in: Advances in Mathematics
publication date: 1992-09-27T00:00:00Z
review text: A space of homogeneous type is a triple \((X,d,\mu)\), where \(d(x,y)\) is a quasi-distance and the measure \(\mu\) satisfies the condition: there exists a finite constant \(A>0\) such that \[ \mu\bigl(B_ d(x,2Kr)\bigr)\leq A\mu\bigl(B_ d(x,r)\bigr) \] holds for every \(x\in X\) and \(r>0\), where \(B_ d(x,r)\) is a ball. The properties of a space of homogeneous type are established. Singular integral operators \(T\) with non-necessarily bounded kernels on spaces of homogeneous type are studied. A criterion for \(T\) to be weakly bounded is obtained. An application to operators defined by principal value integrals gives a priori Lipschitz estimates for some parabolic differential equations.
reviewed by: B. P. Osilenker
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 45P05
zbMATH DE Number: 62679
zbMATH Keywords: singular integral operator
zbMATH Keywords: Lipschitz condition
zbMATH Keywords: weak boundedness
zbMATH Keywords: space of homogeneous type
zbMATH Keywords: parabolic differential equations
MaRDI profile type: Publication
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full work available at URL: 0001-8708(92)90024-f
OpenAlex ID: W1988091634
description: scientific article; zbMATH DE number 62679