Abstract
We present some new results on analytic Ornstein-Uhlenbeck semigroups and use them to extend recent work of Da Prato and Lunardi for Ornstein-Uhlenbeck semigroups on open domains O to the non-symmetric case. Denoting the generator of the semigroup by L_O, we obtain sufficient conditions in order that the domain Dom(\sqrt{-L_O}) be a first order Sobolev space.
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