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Dimension-independent Harnack inequalities for subordinated semigroups. (English) Zbl 1219.43006
Authors’ 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 $$\alpha \in(\frac{1}{2}, 1)$$, and it satisfies the log-Harnack inequality for all $$\alpha \in (0,1)$$. Some infinite-dimensional examples are also presented.

MSC:
 43A80 Analysis on other specific Lie groups 58J65 Diffusion processes and stochastic analysis on manifolds 60J60 Diffusion processes
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