Characterizations for fractional Hardy inequality (1308.1886v2)

Abstract: We provide a Maz'ya type characterization for a fractional Hardy inequality. As an application, we show that a bounded open set $G$ admits a fractional Hardy inequality if and only if the associated fractional capacity is quasiadditive with respect to Whitney cubes of $G$ and the zero extension operator acting on $C_c(G)$ is bounded in an appropriate manner.