Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 4 (2005) no. 4, pp. 729-748.

Replacing the gaussian semigroup in the heat kernel estimates by the Ornstein-Uhlenbeck semigroup on d , we define the notion of Kolmogorov kernel estimates. This allows us to show that under Dirichlet boundary conditions Ornstein-Uhlenbeck operators are generators of consistent, positive, (quasi-) contractive C 0 -semigroups on L p (Ω) for all 1p< and for every domain Ω d . For exterior domains with sufficiently smooth boundary a result on the location of the spectrum of these operators is also given.

Classification: 47D06,  35K20
Haller-Dintelmann, Robert 1; Wiedl, Julian 1

1 Technische Universität Darmstadt Fachbereich Mathematik Schlossgartenstr. 7 D-64289 Darmstadt, Germany
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Haller-Dintelmann, Robert; Wiedl, Julian. Kolmogorov kernel estimates for the Ornstein-Uhlenbeck operator. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 4 (2005) no. 4, pp. 729-748. http://www.numdam.org/item/ASNSP_2005_5_4_4_729_0/

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