A Marcinkiewicz integral type characterization of the Sobolev space
Functional Analysis
2014-11-12 v2
Abstract
In this paper we present a new characterization of the Sobolev space , 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.
Keywords
Cite
@article{arxiv.1405.6127,
title = {A Marcinkiewicz integral type characterization of the Sobolev space},
author = {Piotr Hajłasz and Zhuomin Liu},
journal= {arXiv preprint arXiv:1405.6127},
year = {2014}
}