Boundedness of multilinear commutators of Calderón-Zygmund operators on Orlicz spaces over non-homogeneous spaces
type: Item
instance of: scholarly article
title: Boundedness of multilinear commutators of Calderón-Zygmund operators on Orlicz spaces over non-homogeneous spaces
zbMATH Open document ID: 1275.47079
author: Xing Fu
author: Wen Yuan
author: Dachun Yang
published in: Taiwanese Journal of Mathematics
publication date: 2013-02-21T00:00:00Z
full work available at URL: http://journal.taiwanmathsoc.org.tw/index.php/TJM/article/view/2638
review text: Let \((\mathcal{X},d,\mu)\) be a non-homogeneous space. In a recent paper of \textit{T. A. Bui} and \textit{X. T. Duong} [J. Geom. Anal. 23, No.~2, 895--932 (2013; Zbl 1267.42013)], the \(L^p(\mu)\)-boundedness of commutators of Calderón-Zygmund operators with RBMO\((\mu)\) functions was obtained under the assumption that there is \(m\in (0,\infty)\) such that \(\lambda(x,ar)=a^m\lambda(x,r)\) for all \(x\in \mathcal{X}\) and \(a,r\in (0,\infty)\), where \(\lambda\) is the dominating function of the measure \(\mu\). In this paper, the authors essentially improve the above result and prove that, without the above condition, the multilinear commutators of Calderón-Zygmund operators with RBMO\((\mu)\) functions are bounded on some Orlicz spaces, including \(L^p(\mu)\) with \(1<p<\infty\). The authors also obtain a weak type estimate for multilinear commutators of Calderón-Zygmund operators with special Orlicz-type functions.
reviewed by: Rui Liu
Mathematics Subject Classification ID: 47B47
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 43A99
zbMATH DE Number: 6137999
zbMATH Keywords: multilinear commutator
zbMATH Keywords: Calderón-Zygmund operator
zbMATH Keywords: non-homogeneous space
zbMATH Keywords: Orlicz space
MaRDI profile type: Publication
OpenAlex ID: W1592911795
DOI: 10.11650/TWJM/1500406848
description: scientific article; zbMATH DE number 6137999