Time regularity for generalized Mehler semigroups

Alessandra Lunardi

Mathematische Nachrichten, 2022, vol. 295, issue 11, 2223-2245

Abstract: We study continuity and Hölder continuity of t↦Ptf$t\mapsto P_tf$, where Pt$P_t$ is a generalized Mehler semigroup in Cb(X)$C_b(X)$, the space of the continuous and bounded functions from a Banach space X to R$\mathbb {R}$, and f∈Cb(X)$f\in C_b(X)$. The generators L of such semigroups are realizations of a class of differential and pseudo‐differential operators, both in finite and in infinite dimension. Examples of operators L to which this theory is applicable include Ornstein–Uhlenbeck operators with fractional diffusion in finite dimension, and Ornstein–Uhlenbeck operators with associated strong‐Feller semigroups, in infinite dimension.

Date: 2022
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https://doi.org/10.1002/mana.202000594

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