New characterizations of weighted Morrey-Campanato spaces
type: Item
instance of: scholarly article
title: New characterizations of weighted Morrey-Campanato spaces
zbMATH Open document ID: 1232.42021
published in: Taiwanese Journal of Mathematics
publication date: 2011-08-25T00:00:00Z
review text: The authors introduce and study weighted Morrey-Campanato spaces \(L(\alpha,q,s,\omega;\mathbb{R}^n);\) here \(\alpha\in (0, \infty), q\in [1, \infty],s\) is a nonnegative integer and \(\omega\) is a Muckenhoupt weight. The classical Morrey-Campanato spaces and the weighted Morrey-Campanato spaces introduced earlier are special cases. The results obtained generalise some of the earlier results in these contexts. It is shown that the spaces \(L(\alpha,q,s,\omega;\mathbb{R}^n)\) are all the same for different values of \(q,\) with equivalent norms. Moreover, these spaces are also equivalent to the weighted Lipschitz spaces \(\Lambda(\alpha, \omega; \mathbb{R}^n)\) introduced for all \(\alpha \in (0, \infty), q\in [1, \infty]\) and integers \(s\geq [n\alpha].\) This, in turn, is used to obtain a new characterisation of the spaces \(L(\alpha,q,s,\omega;\mathbb{R}^n)\) for these values of the parameters.
Mathematics Subject Classification ID: 42B35
Mathematics Subject Classification ID: 46E35
zbMATH DE Number: 5943144
zbMATH Keywords: Muckenhoupt weight
zbMATH Keywords: weighted Morrey-Campanato space
zbMATH Keywords: weighted Lipschitz space
author: Dachun Yang
author: Sibei Yang
reviewed by: K. Parthasarathy
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.11650/twjm/1500406166
OpenAlex ID: W4231557556
DOI: 10.11650/TWJM/1500406166
description: scientific article; zbMATH DE number 5943144