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2017 A Marcinkiewicz integral type characterization of the Sobolev space
Piotr Hajłasz, Zhuomin Liu
Publ. Mat. 61(1): 83-104 (2017). DOI: 10.5565/PUBLMAT_61117_03

Abstract

In this paper we present a new characterization of the Sobolev space $W^{1,p}$, $1\lt p\lt \infty$ 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.

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Piotr Hajłasz. Zhuomin Liu. "A Marcinkiewicz integral type characterization of the Sobolev space." Publ. Mat. 61 (1) 83 - 104, 2017. https://doi.org/10.5565/PUBLMAT_61117_03

Information

Received: 10 March 2015; Published: 2017
First available in Project Euclid: 22 December 2016

zbMATH: 1376.46027
MathSciNet: MR3590115
Digital Object Identifier: 10.5565/PUBLMAT_61117_03

Subjects:
Primary: 46E35
Secondary: 42B25

Keywords: Littlewood--Paley theory , Sobolev Spaces

Rights: Copyright © 2017 Universitat Autònoma de Barcelona, Departament de Matemàtiques

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Vol.61 • No. 1 • 2017
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