Fractional Hardy inequalities and visibility of the boundary
Published inStudia mathematica
© Polska Akademia Nauk 2014. This is a final draft version of an article whose final and definitive form has been published by Polska Akademia Nauk. Published in this repository with the kind permission of the publisher.
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.