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Dimension-Independent Harnack Inequalities for Subordinated Semigroups

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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 \(\alpha \in \left(\frac{1}{2},1 \right)\), and it satisfies the log-Harnack inequality for all α ∈ (0, 1). Some infinite-dimensional examples are also presented.

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Correspondence to Maria Gordina.

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Research of Maria Gordina was supported in part by NSF Grant DMS-0706784.

Research of Michael Röckner was supported in part by the German Science Foundation (DFG) through CRC 701.

Research of Feng-Yu Wang was supported in part by WIMICS, NNSFC (10721091) and the 973-Project.

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Gordina, M., Röckner, M. & Wang, FY. Dimension-Independent Harnack Inequalities for Subordinated Semigroups. Potential Anal 34, 293–307 (2011). https://doi.org/10.1007/s11118-010-9198-5

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  • DOI: https://doi.org/10.1007/s11118-010-9198-5

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