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 with the boundedness of extension operators for fractional Sobolev spaces.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-1-3,
author = {Lizaveta Ihnatsyeva and Juha Lehrb\"ack and Heli Tuominen and Antti V. V\"ah\"akangas},
title = {Fractional Hardy inequalities and visibility of the boundary},
journal = {Studia Mathematica},
volume = {223},
year = {2014},
pages = {47-80},
zbl = {1325.46040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-1-3}
}
Lizaveta Ihnatsyeva; Juha Lehrbäck; Heli Tuominen; Antti V. Vähäkangas. Fractional Hardy inequalities and visibility of the boundary. Studia Mathematica, Tome 223 (2014) pp. 47-80. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm224-1-3/