Nonautonomous Ornstein-Uhlenbeck operators in weighted spaces of continuous functions

We consider the nonautonomous Ornstein-Uhlenbeck operator in some weighted spaces of continuous functions in ℝN. We prove sharp uniform estimates for the spatial derivatives of the associated evolution operator Ps,t, which we use to prove optimal Schauder estimates for the solution to some nonhomogeneous parabolic Cauchy problems associated with the Ornstein-Uhlenbeck operator. We also prove that, for any t>s, the evolution operator Ps,t is compact in the previous weighted spaces. © 2013 Springer Science+Business Media New York.