Compactness characterization of commutators for Littlewood-Paley operators
type: Item
instance of: scholarly article
title: Compactness characterization of commutators for Littlewood-Paley operators
zbMATH Open document ID: 1205.42012
published in: Kodai Mathematical Journal
publication date: 2009-08-24T00:00:00Z
review text: Let \(L\) denote one of the Littlewood-Paley operators, such as the Littlewood-Paley \(g\)-function, the Lusin area integral and the Littlewood-Paley \(g^*_{\lambda}\)-function. The authors prove that the commutator \([b,L]\) is a compact operator in \(L^p(R^n)\) if and only if \(b\in\) VMO\((\mathbb{R}^n)\). The Littlewood-Paley operators discussed in this paper are nonlinear, which requires different techniques from traditional methods (such as in [\textit{A. Uchiyama}, Tohoku Math. J., II. Ser. 30, 163--171 (1978; Zbl 0384.47023)]). Their work is thoughtful and innovative.
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 5598067
zbMATH Keywords: Littlewood-Paley operators
zbMATH Keywords: commutators
zbMATH Keywords: compactness
zbMATH Keywords: BMO
zbMATH Keywords: VMO
author: Yanping Chen
author: Yong Ding
reviewed by: Lizhong Peng
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2996/kmj/1245982907
OpenAlex ID: W1996814995
DOI: 10.2996/KMJ/1245982907
description: scientific article; zbMATH DE number 5598067