Invariant measures and maximal L2 regularity for nonautonomous Ornstein-Uhlenbeck equations

We characterize the domain of the realizations of a linear parabolicoperator defined in L² spaces with respect to a suitable measurethat is invariant for the associated evolution semigroup. Asa byproduct, we obtain optimal L² regularity results for evolutionequations with time-dependant Ornstein–Uhlenbeck operators.