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 α satisfies a dimension-free Harnack inequality provided α ∈(1/2, 1), and it satisfies the log-Harnack inequality for all α ∈ (0,1). Some infinite-dimensional examples are also presented.
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