An analytical proof of Hardy-like inequalities related to the Dirac operator

TL;DR

This paper provides a direct and elementary proof of sharp Hardy-like inequalities associated with the Dirac operator, improving understanding of potential asymptotics without relying on spectral analysis.

Contribution

It introduces new elementary methods to establish sharp Hardy inequalities related to the Dirac operator under optimal asymptotic conditions.

Findings

Established sharp Hardy inequalities for the Dirac operator

Provided elementary proofs avoiding spectral analysis

Identified optimal conditions on potential asymptotics

Abstract

We prove some sharp Hardy type inequalities related to the Dirac operator by elementary, direct methods. Some of these inequalities have been obtained previously using spectral information about the Dirac-Coulomb operator. Our results are stated under optimal conditions on the asymptotics of the potentials near zero and near infinity.