A Marcinkiewicz integral type characterization of the Sobolev space
- Autores: Piotr Hajlasz, Zhuomin Liu
- Localización: Publicacions matematiques, ISSN 0214-1493, Vol. 61, Nº 1, 2017, págs. 83-104
- Idioma: inglés
- DOI: 10.5565/10.5565_PUBLMAT_61117_03
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Resumen
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.
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