Fractional Hardy-Sobolev-Maz'ya inequality for domains

Abstract

We prove a fractional version of the Hardy--Sobolev--Maz'ya inequality for arbitrary domains and $L^p$ norms with $p\ge 2$. This inequality combines the fractional Sobolev and the fractional Hardy inequality into a single inequality, while keeping the sharp constant in the Hardy inequality.

14 pages

References in corpus (1)

• The fractional Hardy inequality with a remainder term

Cited by in corpus (2)

• Hardy and Poincaré inequalities in fractional Orlicz-Sobolev spaces
• Study of fractional Poincaré inequalities on unbounded domains