Finsler Hardy-Kato's inequality

TL;DR

This paper extends the Hardy-Kato inequality to Finsler geometry, providing an improved trace inequality on half-spaces and exploring its validity on open cones, thus broadening the scope of classical inequalities.

Contribution

It introduces a Finsler version of the Hardy-Kato inequality, extending previous Euclidean results and analyzing its applicability to open cones.

Findings

Established a Finsler Hardy-Kato inequality on half-spaces.

Extended the inequality to open cones.

Demonstrated the inequality's validity in the Finsler setting.

Abstract

We prove an improved version of the trace-Hardy inequality, so-called Kato's inequality, on the half-space in Finsler context. The resulting inequality extends the former one obtained by \cite{AFV} in Euclidean context. Also we discuss the validity of the same type of inequalities on open cones.