Heat kernel estimates for subordinate Markov processes and their applications

TL;DR

This paper derives precise estimates for transition densities of subordinate Markov processes and demonstrates their implications for Harnack inequalities, regularity, and Green function estimates in potential theory.

Contribution

It provides sharp two-sided estimates for transition densities and applies these results to establish key inequalities and regularity properties for subordinate Markov processes.

Findings

Sharp two-sided transition density estimates

Harnack inequality and Hölder regularity for parabolic functions

Precise Green function estimates

Abstract

In this paper, we establish sharp two-sided estimates for transition densities of a large class of subordinate Markov processes. As applications, we show that the parabolic Harnack inequality and H\"older regularity hold for parabolic functions of such processes, and derive sharp two-sided Green function estimates.