A Marcinkiewicz integral type characterization of the Sobolev space

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Title:	A Marcinkiewicz integral type characterization of the Sobolev space
Author:	Hajlasz, Piotr; Liu, Zhuomin
Abstract:	In this paper we present a new characterization of the Sobolev space W1,p , 1 < p < ∞ which is a higher dimensional version of a result of Waterman [32]. We also provide a new and simplified proof of a recent result of Alabern, Mateu, and Verdera [2]. Finally, we generalize the results to the case of weighted Sobolev spaces with respect to a Muckenhoupt weight.
Subject(s):	-Sobolev spaces -Littlewood-paley theory
Rights:	open access Tots els drets reservats. https://rightsstatements.org/vocab/InC/1.0/
Document type:	Article
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Uri:	https://ddd.uab.cat/record/168345