Fractional Hardy inequalities and visibility of the boundary
Classical Analysis and ODEs
2015-12-23 v2
Abstract
We prove fractional order Hardy inequalities on open sets under a combined fatness and visibility condition on the boundary. We demonstrate by counterexamples that fatness conditions alone are not sufficient for such Hardy inequalities to hold. In addition, we give a short exposition of various fatness conditions related to our main result, and apply fractional Hardy inequalities in connection to the boundedness of extension operators for fractional Sobolev spaces.
Keywords
Cite
@article{arxiv.1305.4616,
title = {Fractional Hardy inequalities and visibility of the boundary},
author = {Lizaveta Ihnatsyeva and Juha Lehrbäck and Heli Tuominen and Antti V. Vähäkangas},
journal= {arXiv preprint arXiv:1305.4616},
year = {2015}
}
Comments
30 pages, 3 figures. Minor revisions to the previous version. To be published in Studia Math