Let be the Ornstein-Uhlenbeck operator which is self-adjoint with respect to the Gauss measure on We prove a sharp estimate of the operator norm of the imaginary powers of on Then we use this estimate to prove that if is in and is a bounded holomorphic function in the sector and satisfies a Hörmander-like condition of (nonintegral) order greater than one on the boundary, then the operator is bounded on This improves earlier results of the authors with J. García-Cuerva and J.L. Torrea.
@article{ASNSP_2004_5_3_3_447_0, author = {Mauceri, Giancarlo and Meda, Stefano and Sj\"ogren, Peter}, title = {Sharp estimates for the Ornstein-Uhlenbeck operator}, journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 3}, number = {3}, year = {2004}, pages = {447-480}, zbl = {1116.47036}, mrnumber = {2099246}, language = {en}, url = {http://www.numdam.org/item/ASNSP_2004_5_3_3_447_0} }
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://www.numdam.org/item/ASNSP_2004_5_3_3_447_0/
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