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Nonautonomous Ornstein-Uhlenbeck operators in weighted spaces of continuous functions

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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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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi di Milano Bicocca, Via Cozzi, 53, 20155, Milan, Italy

    Davide Addona

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  1. Davide Addona
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Correspondence to Davide Addona.

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Communicated by Abdelaziz Rhandi.

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Addona, D. Nonautonomous Ornstein-Uhlenbeck operators in weighted spaces of continuous functions. Semigroup Forum 87, 509–536 (2013). https://doi.org/10.1007/s00233-013-9495-6

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  • DOI: https://doi.org/10.1007/s00233-013-9495-6

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