Dimension-independent Harnack inequalities for subordinated semigroups

Abstract

Dimension-independent Harnack inequalities are derived for a class of subordinate semigroups. In particular, for a diffusion satisfying the Bakry-Emery curvature condition, the subordinate semigroup with power $\alpha$ satisfies a dimension-free Harnack inequality provided $\alpha \in (1/2,1)$, and it satisfies the log-Harnack inequality for all $\alpha \in (0,1).$ Some infinite-dimensional examples are also presented.

References in corpus (1)

• Harnack inequality and applications for stochastic generalized porous media equations