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- W2012175556 abstract "Harnack inequalities are established for a class of generalized Mehler semigroups, which in particular imply upper bound estimates for the transition density. Moreover, Poincaré and log-Sobolev inequalities are proved in terms of estimates for the square field operators. Furthermore, under a condition, well-known in the Gaussian case, we prove that generalized Mehler semigroups are strong Feller. The results are illustrated by concrete examples. In particular, we show that a generalized Mehler semigroup with an α-stable part is not hyperbounded but exponentially ergodic, and that the log-Sobolev constant obtained by our method in the special Gaussian case can be sharper than the one following from the usual curvature condition. Moreover, a Harnack inequality is established for the generalized Mehler semigroup associated with the Dirichlet heat semigroup on (0,1). We also prove that this semigroup is not hyperbounded." @default.
- W2012175556 created "2016-06-24" @default.
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- W2012175556 date "2003-09-01" @default.
- W2012175556 modified "2023-09-30" @default.
- W2012175556 title "Harnack and functional inequalities for generalized Mehler semigroups" @default.
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- W2012175556 doi "https://doi.org/10.1016/s0022-1236(03)00165-4" @default.
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