We prove an optimal embedding result for the domains of Kolmogorov (or degenerate hypoelliptic Ornstein--Uhlenbeck) operators in L^2 spaces with respect to invariant measures. We use an interpolation method together with optimal L^2 estimates for the space derivatives of T(t)f near t=0, where T(t) is the Ornstein--Uhlenbeck semigroup and f is any function in L^2.
Invariant measures and maximal L^2 regularity for nonautonomous Ornstein-Uhlenbeck equations / GEISSERT M; LUNARDI A.. - In: JOURNAL OF THE LONDON MATHEMATICAL SOCIETY. - ISSN 0024-6107. - 77(2008), pp. 719-740. [10.1112/jlms/jdn009]