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
• Enlaces
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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.