A Marcinkiewicz integral type characterization of the Sobolev space
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. We also provide a new and simplified proof of a recent result of Alabern, Mateu and Verdera. Finally, we generalize the results to the case of weighted Sobolev spaces with respect to a Muckenhoupt weight.
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