Two consequences of Davies's Hardy inequality

TL;DR

This paper demonstrates how Davies's Hardy inequality can be used to rederive established results by Lieb and Rozenblum, highlighting a new application of this inequality in spectral theory.

Contribution

It introduces a novel approach to deriving classical results using Davies's Hardy inequality, connecting different areas of mathematical analysis.

Findings

Re-derivation of Lieb and Rozenblum's results using Davies's Hardy inequality

Establishment of a new link between Hardy inequalities and spectral estimates

Simplification of proofs for well-known spectral bounds

Abstract

In this short note we would like to show that one can use Davies's Hardy inequality to rederive well-known results of Lieb and Rozenblum.