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, p. 471-485
We show that the domain of the Ornstein-Uhlenbeck operator on L p ( N ,μdx) equals the weighted Sobolev space W 2,p ( N ,μdx), where μdx 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, Série 5, Tome 1 (2002) no. 2, pp. 471-485. http://www.numdam.org/item/ASNSP_2002_5_1_2_471_0/

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