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The domain of the Ornstein-Uhlenbeck operator on an $$L^p$$-space with invariant measure. (English) Zbl 1170.35375
Summary: We show that the domain of the Ornstein-Uhlenbeck operator on $$L^p$$ $$(\mathbb{R}^,\mu dx)$$ equals the weighted Sobolev space $$W^{2,p} (\mathbb{R}^N,\mu dx)$$, 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.

##### MSC:
 35J15 Second-order elliptic equations 35K10 Second-order parabolic equations 47A55 Perturbation theory of linear operators 47D06 One-parameter semigroups and linear evolution equations
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