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

Metafune, Giorgio; Prüss, Jan; Rhandi, Abdelaziz; Schnaubelt, Roland

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 1 (2002) no. 2, pp. 471-485.

We show that the domain of the Ornstein-Uhlenbeck operator on $L^p$ $({ℝ}^N,\mu dx)$ equals the weighted Sobolev space $W^{2,p}({ℝ}^N,\mu dx)$, 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.

Classification : 35J15, 35K10, 47A55, 47D06

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