Dimension-independent Harnack inequalities for subordinated semigroups

2010/04/18 by Maria Gordina, Michael Röckner, Gordina, Maria +4
Mathematics · #58G32 #58J65 #60G51 #60J60} #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations #Point processes and geometric inequalities #Probability (math.PR) #math.PR #msc:58G32 #msc:58J65 #msc:60G51

paper · pdf · doi:10.48550/arxiv.1004.3016

arxiv created 2010/04/18 · openalex publication_date 2010/04/18 · arxiv updated 2010/04/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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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