The domain of the Ornstein-Uhlenbeck operator on an ${L}^{p}$-space with invariant measure
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 2, p. 471-485

We show that the domain of the Ornstein-Uhlenbeck operator on ${L}^{p}$ $\left({ℝ}^{N},\mu dx\right)$ equals the weighted Sobolev space ${W}^{2,p}\left({ℝ}^{N},\mu dx\right)$, 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
@article{ASNSP_2002_5_1_2_471_0,
author = {Metafune, Giorgio and Pr\"uss, Jan and Rhandi, Abdelaziz and Schnaubelt, Roland},
title = {The domain of the Ornstein-Uhlenbeck operator on an $L^p$-space with invariant measure},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {2},
year = {2002},
pages = {471-485},
zbl = {1170.35375},
mrnumber = {1991148},
language = {en},
url = {http://www.numdam.org/item/ASNSP_2002_5_1_2_471_0}
}

Metafune, Giorgio; Prüss, Jan; Rhandi, Abdelaziz; Schnaubelt, Roland. The domain of the Ornstein-Uhlenbeck operator on an $L^p$-space with invariant measure. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 1 (2002) no. 2, pp. 471-485. http://www.numdam.org/item/ASNSP_2002_5_1_2_471_0/

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