Abstract
The Harnack inequality established in Röckner and Wang (J Funct Anal 203:237–261, 2003) for generalized Mehler semigroup is improved and generalized. As applications, the log-Harnack inequality, the strong Feller property, the hyper-bounded property, and some heat kernel inequalities are presented for a class of O-U type semigroups with jump. These inequalities and semigroup properties are indeed equivalent, and thus sharp, for the Gaussian case. As an application of the log-Harnack inequality, the HWI inequality is established for the Gaussian case. Perturbations with linear growth are also investigated.
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Supported in part by WIMICS, SRFDP, the Fundamental Research Funds for the Central Universities, the DFG through SFB-701 and IRTG 1132.
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Ouyang, SX., Röckner, M. & Wang, FY. Harnack Inequalities and Applications for Ornstein–Uhlenbeck Semigroups with Jump. Potential Anal 36, 301–315 (2012). https://doi.org/10.1007/s11118-011-9231-3
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DOI: https://doi.org/10.1007/s11118-011-9231-3