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arXiv · 1405.6127

A Marcinkiewicz integral type characterization of the Sobolev space

Piotr Hajłasz·Zhuomin Liu
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Abstract

In this paper we present a new characterization of the Sobolev space $W^{1,p}$, $1<p<\infty$ 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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Piotr Hajłasz, Zhuomin Liu. 2014-11-11. A Marcinkiewicz integral type characterization of the Sobolev space. https://arxiv.org/abs/1405.6127

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