Fractional Hardy inequalities and visibility of the boundary
Volume 224 / 2014
Studia Mathematica 224 (2014), 47-80
MSC: Primary 46E35; Secondary 26D15.
DOI: 10.4064/sm224-1-3
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 with the boundedness of extension operators for fractional Sobolev spaces.
