Nonautonomous Ornstein-Uhlenbeck operators in weighted spaces of continuous functions |
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Authors: | Davide Addona |
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Affiliation: | 1. Dipartimento di Matematica, Università degli Studi di Milano Bicocca, Via Cozzi, 53, 20155, Milan, Italy
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Abstract: | We consider the nonautonomous Ornstein-Uhlenbeck operator in some weighted spaces of continuous functions in $mathbb{R}^{N}$ . We prove sharp uniform estimates for the spatial derivatives of the associated evolution operator P s,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 P s,t is compact in the previous weighted spaces. |
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