Hardy inequalities and non-explosion results for semigroups

TL;DR

This paper establishes non-explosion conditions for certain Schrödinger-perturbed semigroups and derives Hardy inequalities for their quadratic forms using explicit supermedian functions.

Contribution

It introduces new non-explosion criteria and Hardy inequalities for Schrödinger-perturbed symmetric semigroups based on explicit supermedian functions.

Findings

Non-explosion results for Schrödinger-perturbed semigroups

Hardy inequalities for quadratic forms of these semigroups

Use of explicit supermedian functions in proofs

Abstract

We prove non-explosion results for Schr\"odinger perturbations of symmetric transition densities and Hardy inequalities for their quadratic forms by using explicit supermedian functions of their semigroups.