Abstract
AbstractWe study continuity and Hölder continuity of , where is a generalized Mehler semigroup in , the space of the continuous and bounded functions from a Banach space X to , and . 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.
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