Fractional Hardy-Sobolev type inequalities for half spaces and John domains

TL;DR

This paper establishes a new fractional Hardy-Sobolev-Maz'ya inequality for half spaces and John domains, addressing an open question and expanding the inequality's applicability to more general unbounded domains.

Contribution

It introduces a novel version of the fractional Hardy-Sobolev inequality applicable to half spaces and John domains, solving a recent open problem.

Findings

Proved a fractional Hardy-Sobolev-Maz'ya inequality for half spaces.

Extended the inequality to general unbounded John domains.

Provided a complete answer to an open question by Musina and Nazarov.

Abstract

As our main result we prove a variant of the fractional Hardy-Sobolev-Maz'ya inequality for half spaces. This result contains a complete answer to a recent open question by Musina and Nazarov. In the proof we apply a new version of the fractional Hardy-Sobolev inequality that we establish also for more general unbounded John domains than half spaces.