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We show that the domain of the Ornstein-Uhlenbeck operator on equals the weighted Sobolev space , where is the corresponding invariant measure. Our approach relies on the operator sum method, namely the commutative and the non commutative Dore-Venni theorems.
@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},
publisher = {Scuola normale superiore},
volume = {Ser. 5, 1},
number = {2},
year = {2002},
mrnumber = {1991148},
zbl = {1170.35375},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_471_0/}
}
TY - JOUR AU - Metafune, Giorgio AU - Prüss, Jan AU - Rhandi, Abdelaziz AU - Schnaubelt, Roland TI - The domain of the Ornstein-Uhlenbeck operator on an $L^p$-space with invariant measure JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2002 SP - 471 EP - 485 VL - 1 IS - 2 PB - Scuola normale superiore UR - http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_471_0/ LA - en ID - ASNSP_2002_5_1_2_471_0 ER -
%0 Journal Article %A Metafune, Giorgio %A Prüss, Jan %A Rhandi, Abdelaziz %A Schnaubelt, Roland %T The domain of the Ornstein-Uhlenbeck operator on an $L^p$-space with invariant measure %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2002 %P 471-485 %V 1 %N 2 %I Scuola normale superiore %U http://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_471_0/ %G en %F 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://geodesic.mathdoc.fr/item/ASNSP_2002_5_1_2_471_0/