We prove a Hardy inequality for the fractional Laplacian on the interval with the optimal constant and additional lower order term. As a consequence, we also obtain a fractional Hardy inequality with the best constant and an extra lower order term for general domains, following the method of M. Loss and C. Sloane [J. Funct. Anal. 259 (2010)].
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm122-1-6,
author = {Bart\l omiej Dyda},
title = {Fractional Hardy inequality with a remainder term},
journal = {Colloquium Mathematicae},
volume = {122},
year = {2011},
pages = {59-67},
zbl = {1228.26022},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm122-1-6}
}
Bartłomiej Dyda. Fractional Hardy inequality with a remainder term. Colloquium Mathematicae, Tome 122 (2011) pp. 59-67. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm122-1-6/