A Marcinkiewicz integral type characterization of the Sobolev space

A Marcinkiewicz integral type characterization of the Sobolev space

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...

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Hauptverfasser: Hajlasz, Piotr, Liu, Zhuomin
Format: Artikel
Sprache:eng
Schlagworte:
Littlewood-paley theory
Sobolev spaces
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Zusammenfassung: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.