Fractional Hardy-type inequalities in domains with plump complement

TL;DR

This paper proves fractional Hardy inequalities in bounded domains with specific geometric properties, broadening the understanding of such inequalities in smooth and Lipschitz domains.

Contribution

It introduces new fractional Hardy inequalities applicable to domains with plump complements, including smooth and Lipschitz domains.

Findings

Established fractional Hardy inequalities in bounded domains with plump complements.

Extended applicability to C^ and Lipschitz domains.

Provided mathematical framework for inequalities in complex geometric settings.

Abstract

We establish fractional Hardy-type inequalities in a bounded domain with plump complement. In particular our results apply in bounded C^\infty domains and Lipschitz domains.