Continuity properties for linear commutators of Calderón-Zygmund operators
type: Item
instance of: scholarly article
title: Continuity properties for linear commutators of Calderón-Zygmund operators
zbMATH Open document ID: 0926.42013
published in: Collectanea Mathematica
publication date: 1998-09-23T00:00:00Z
full work available at URL: https://eudml.org/doc/41081
review text: It is known that the linear commutator \([b,T]\) of a Calderón-Zygmund operator \(T\) with a BMO function \(b\) does not satisfy some of the continuity properties typical for a Calderón-Zygmund operator, for instance, continuity from the Hardy space \(H^p\) into \(L^p\) for \(p\leq 1\) large enough, and weak type \((1,1)\). We obtain in this paper alternative results. Indeed, we prove in the first part of the paper that \([b,T]\) is continuous from \(H_b^p\) into \(L^p\), where \(H_b^p\) denotes an atomic space with atoms satisfying an extra cancellation condition involving the function \(b\). In the second part of the paper we define a weak version \(H_b^{p,\infty}\) of this atomic space and we prove that \([b,T]\) maps continuously \(H_b^{p,\infty}\) into \(L^{p,\infty}\).
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B30
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 1186310
zbMATH Keywords: Calderón-Zygmund operators
zbMATH Keywords: commutators
zbMATH Keywords: BMO
zbMATH Keywords: atomic spaces
author: Josefina Alvarez Alonso
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1186310