Boundedness for the commutator of convolution operator
type: Item
instance of: scholarly article
title: Boundedness for the commutator of convolution operator
zbMATH Open document ID: 1029.47030
DOI: 10.1016/S0022-247X(03)00029-5
author: Lin Tang
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-25T00:00:00Z
review text: The author considers the operators which are defined as follows: \[ (T_{b,m}f)(x) = \int_{\mathbb{R}} [b(x)-b(y)]^{m}\frac{\Omega(x-y)}{|x-y|^{n}}f(y) dy, \] and the corresponding maximal operator of the form \[ (T_{b,m}^{\ast}f)(x) = \sup_{\varepsilon>0} \left|\int_{|x-y|>\varepsilon} [b(x)-b(y)]^{m}\frac{\Omega(x-y)}{|x-y|^{n}}f(y) dy \right|. \] The boundedness of these operators is considered in the homogeneous Herz space, which is a generalization of the weighted Lebesgue spaces with power weight.
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 47G10
Mathematics Subject Classification ID: 47B38
zbMATH DE Number: 1915769
zbMATH Keywords: commutator
zbMATH Keywords: convolution operator
zbMATH Keywords: Herz space
MaRDI profile type: Publication
cites work: Equivalent Norms for Sobolev Spaces
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description: scientific article; zbMATH DE number 1915769