Hardy inequalities with homogenuous weights

TL;DR

This paper establishes sharp Hardy inequalities involving weight functions with potential singularities on the unit sphere, utilizing recent eigenvalue bounds for Schrödinger operators.

Contribution

It introduces new Hardy inequalities with singular weights on the sphere, extending previous results with sharp constants and eigenvalue techniques.

Findings

Derived sharp Hardy inequalities with singular weights

Utilized eigenvalue bounds for Schrödinger operators on the sphere

Extended classical inequalities to include singular weight functions

Abstract

In this paper we obtain some sharp Hardy inequalities with weight functions that may admit singularities on the unit sphere. In order to prove the main results of the paper we use some recent sharp inequalities for the lowest eigenvalue of Schr\"odinger operators on the unit sphere obtaind in the paper [DEL].