Sharp Hardy inequalities for Sobolev-Bregman forms

TL;DR

This paper establishes precise fractional Hardy inequalities for the half-space and convex domains, extending previous results to Sobolev-Bregman forms, thereby advancing the mathematical understanding of these inequalities.

Contribution

It introduces sharp fractional Hardy inequalities for Sobolev-Bregman forms in specific domains, expanding the scope of prior inequalities.

Findings

Sharp fractional Hardy inequalities for the half-space.

Extension of results to convex domains.

Generalization to Sobolev-Bregman forms.

Abstract

We obtain sharp fractional Hardy inequalities for the half-space and for convex domains. We extend the results of Bogdan and Dyda and of Loss and Sloane to the setting of Sobolev-Bregman forms.