The domain of the Ornstein-Uhlenbeck operator on an $L^p$-space with invariant measure

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Annali della Scuola Normale Superiore di Pisa- Classe di Scienze 1 (2):471-485 (2002)
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Abstract

We show that the domain of the Ornstein-Uhlenbeck operator on $L^p$ $$ equals the weighted Sobolev space $W^{2,p}$, where $\mu dx$ is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems

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Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator.Robert Haller-Dintelmann & Julian Wiedl - 2005 - Annali della Scuola Normale Superiore di Pisa- Classe di Scienze 4 (4):729-748.

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