On the perturbation of positive semigroups

TL;DR

This paper extends heat kernel estimates and domination results for positive semigroups, providing a broader perturbation framework applicable to Dirichlet forms and $L_p$-spaces.

Contribution

It introduces a perturbation result for positive semigroups, generalizing existing heat kernel estimates and domination principles.

Findings

Extended heat kernel estimate to positive semigroups

Generalized domination for semigroups on $L_p$-spaces

Provided a perturbation framework for Dirichlet forms

Abstract

We prove a perturbation result for positive semigroups, thereby extending a heat kernel estimate by Barlow, Grigor'yan and Kumagai for Dirichlet forms (\cite{bgk2009}) to positive semigroups. This also leads to a generalization of domination for semigroups on $L_p$-spaces.