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We characterize the domain of the realizations of a linear parabolic operator  defined in  L  2  spaces with respect to a suitable measure that is invariant for the associated evolution semigroup. As a byproduct, we obtain optimal  L  2  regularity results for evolution equations with time‐dependant Ornstein–Uhlenbeck operators.

Invariant measures and maximal L 2 regularity for nonautonomous Ornstein–Uhlenbeck equations