Hardy type estimates for commutators of fractional integrals
type: Item
instance of: scholarly article
title: Hardy type estimates for commutators of fractional integrals
zbMATH Open document ID: 1245.42016
DOI: 10.1216/RMJ-2011-41-1-319
author: Yueshan Wang
author: Yuexiang He
published in: Rocky Mountain Journal of Mathematics
publication date: 2011-03-01T00:00:00Z
review text: Inspired by \textit{Y. Sun} and \textit{W. Su} [J. Funct. Anal. 234, No. 2, 235--260 (2006; Zbl 1156.42306)], the authors obtain sufficient conditions for the boundedness of commutator operators \[ [b,I_\alpha](f)(x):=b(x)\,I_\alpha(f)(x)-I_\alpha(bf)(x) \] (\(b\) being from \(BMO(\mathbb R^n)\) or \(LMO(\mathbb R^n)\)) from the local Hardy spaces \(h^p(\mathbb R^n)\) into spaces \(h^p_q(\mathbb R^n):=h^p(\mathbb R^n)+L^q(\mathbb R^n)\), where \(0<\alpha<n\), \(q>n/(n-\alpha)\), \(n/(n+\alpha)<p<1\) or \(p=1\), associated with the fractional integral \[ I_\alpha f(x):=\int_{\mathbb R^n}\frac{f(y)}{|x-y|^{n-\alpha}}\,dy. \]
reviewed by: Petr Gurka
Mathematics Subject Classification ID: 42B20
Mathematics Subject Classification ID: 42B25
zbMATH DE Number: 5858894
zbMATH Keywords: fractional integral
zbMATH Keywords: commutator
zbMATH Keywords: Hardy space
zbMATH Keywords: local Hardy space
zbMATH Keywords: BMO
zbMATH Keywords: LMO
MaRDI profile type: Publication
cites work: On \(BMO\) regularity for linear elliptic systems
cites work: Q3036042
cites work: \(H^p\) spaces of several variables
cites work: A local version of real Hardy spaces
cites work: Boundedness of commutators of fractional and singular integrals for the extreme values of \(p\)
cites work: On functions of bounded mean oscillation
cites work: A characterization of $H^{p}(R^{n})$ in terms of atoms
cites work: Q4848732
cites work: Q5597805
cites work: Interior \(h^1\)-estimates for second order elliptic equations with vanishing \(LMO\) coefficients
cites work: Hardy type estimates for commutators of singular integrals
full work available at URL: rmj-2011-41-1-319
OpenAlex ID: W2055532849
description: scientific article; zbMATH DE number 5858894