Sharp estimates for the Ornstein-Uhlenbeck operator
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 3, pp. 447-480.

Let be the Ornstein-Uhlenbeck operator which is self-adjoint with respect to the Gauss measure γ on d . We prove a sharp estimate of the operator norm of the imaginary powers of on L p (γ), 1<p<. Then we use this estimate to prove that if b is in [0,) and M is a bounded holomorphic function in the sector {z:modarg(z-b)<arcsin|2/p-1|} and satisfies a Hörmander-like condition of (nonintegral) order greater than one on the boundary, then the operator M() is bounded on L p (γ). This improves earlier results of the authors with J. García-Cuerva and J.L. Torrea.

Classification: 47A60, 47D03, 60G15
Mauceri, Giancarlo 1; Meda, Stefano 2; Sjögren, Peter 3

1 Dipartimento di Matematica       Università di Genova via Dodecaneso 35 16146 Genova, Italy
2 Dipartimento di Matematica e Applicazioni Università di Milano-Bicocca via Bicocca degli Arcimboldi 8 20126 Milano, Italy
3 Department of Mathematics Göteborg University SE-412 96 Göteborg, Sweden
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     title = {Sharp estimates for the {Ornstein-Uhlenbeck} operator},
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Mauceri, Giancarlo; Meda, Stefano; Sjögren, Peter. Sharp estimates for the Ornstein-Uhlenbeck operator. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 3, pp. 447-480. http://archive.numdam.org/item/ASNSP_2004_5_3_3_447_0/

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