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

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

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

Résumé

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

MR Zbl | 1 citation dans Numdam

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},
     pages = {471--485},
     year = {2002},
     publisher = {Scuola normale superiore},
     volume = {Ser. 5, 1},
     number = {2},
     mrnumber = {1991148},
     zbl = {1170.35375},
     language = {en},
     url = {https://www.numdam.org/item/ASNSP_2002_5_1_2_471_0/}
}

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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, Série 5, Tome 1 (2002) no. 2, pp. 471-485. https://www.numdam.org/item/ASNSP_2002_5_1_2_471_0/

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