Perturbations of positive semigroups on $L_p$-spaces

TL;DR

This paper characterizes how positive semigroups on different Lp-spaces relate through variation of constants estimates, with applications to kernel estimates for semigroups from accretive and non-local forms.

Contribution

It provides a new characterization linking semigroup estimates to generator and resolvent estimates, extending understanding of positive semigroup relations.

Findings

Characterization of semigroup relations via generator and resolvent estimates

Application to kernel estimates for semigroups from accretive and non-local forms

Extension of variation of constants estimates to different Lp-spaces

Abstract

We give a characterization of a variation of constants type estimate relating two positive semigroups on (possibly different) $L_p$-spaces to one another in terms of corresponding estimates for the respective generators and of estimates for the respective resolvents. The results have applications to kernel estimates for semigroups induced by accretive and non-local forms on $\sigma$-finite measure spaces.