On fractional Orlicz boundary Hardy inequalities

TL;DR

This paper studies fractional Orlicz boundary Hardy inequalities, extending classical results to fractional and Orlicz settings, including critical cases with logarithmic corrections across various Lipschitz domains.

Contribution

It establishes new fractional Orlicz boundary Hardy inequalities, including critical cases with logarithmic corrections, for a broad class of Lipschitz domains.

Findings

Proved fractional Orlicz boundary Hardy inequalities for bounded Lipschitz domains.

Derived inequalities with logarithmic corrections for critical cases.

Extended results to domains above Lipschitz graphs and complements of Lipschitz domains.

Abstract

We investigate the fractional Orlicz boundary Hardy-type inequality for bounded Lipschitz domains. Further, we establish fractional Orlicz boundary Hardy-type inequalities with logarithmic corrections for specific critical cases across various domains, such as bounded Lipschitz domains, domains above the graph of a Lipschitz function, and the complement of a bounded Lipschitz domain.