Singular integrals and commutators on homogeneous groups
type: Item
instance of: scholarly article
title: Singular integrals and commutators on homogeneous groups
zbMATH Open document ID: 1026.43007
DOI: 10.1023/A:1016568918973
author: Guozhen Lu
author: Shanzhen Lu
author: Dachun Yang
published in: Analysis Mathematica
publication date: 2003-10-14T00:00:00Z
review text: The authors using the basic idea from the paper of \textit{F. Soria} and \textit{G. Weiss} [Indiana Univ. Math. J. 43, 187-204 (1994; Zbl 0803.42004)], prove several general theorems for the boundedness of sublinear operators and commutators generated by linear operators and \(\text{BMO}({\mathbf G})\) functions on the weighted Lebesgue space on the homogeneous group \({\mathbf G}\). The conditions of these theorems are so general that many important operators in analysis satisfy these conditions. Some of these theorems are best possible even for \(n\)-dimensional Euclidean spaces. They also establish some new applications of these theorems on weighted inequalities for singular integrals (including rough singular integral operators, oscillatory integrals, parabolic singular integrals) and their commutators and the maximal operators associated with them. These methods are more direct than previously used methods.
Mathematics Subject Classification ID: 43A85
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 1992693
zbMATH Keywords: singular integral
zbMATH Keywords: commutator
zbMATH Keywords: homogeneous group
zbMATH Keywords: Muckenhoupt classes
zbMATH Keywords: rough singular integral operators
zbMATH Keywords: oscillatory integrals
zbMATH Keywords: maximal operators
reviewed by: Amiran Gogatishvili
MaRDI profile type: Publication
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full work available at URL: a:1016568918973
OpenAlex ID: W33753585
description: scientific article; zbMATH DE number 1992693