A Marcinkiewicz integral type characterization of the Sobolev space

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dc.contributor.author	Hajlasz, Piotr
dc.contributor.author	Liu, Zhuomin
dc.date	2017
dc.identifier	https://ddd.uab.cat/record/168345
dc.identifier	urn:10.5565/PUBLMAT_61117_03
dc.identifier	urn:oai:ddd.uab.cat:168345
dc.identifier	urn:oai:raco.cat:article/316079
dc.identifier	urn:articleid:20144350v61n1p83
dc.identifier	urn:wos_id:000396538700003
dc.format	application/pdf
dc.language	eng
dc.publisher
dc.relation	;
dc.relation	Publicacions matemàtiques ; Vol. 61 Núm. 1 (2017), p. 83-104
dc.rights	open access
dc.rights	Tots els drets reservats.
dc.rights	https://rightsstatements.org/vocab/InC/1.0/
dc.subject	Sobolev spaces
dc.subject	Littlewood-paley theory
dc.title	A Marcinkiewicz integral type characterization of the Sobolev space
dc.type	Article
dc.description.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.