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}, pages = {447--480}, publisher = {Scuola Normale Superiore, Pisa}, volume = {Ser. 5, 3}, number = {3}, year = {2004}, mrnumber = {2099246}, zbl = {1116.47036}, language = {en}, url = {http://archive.numdam.org/item/ASNSP_2004_5_3_3_447_0/} }
TY - JOUR AU - Mauceri, Giancarlo AU - Meda, Stefano AU - Sjögren, Peter TI - Sharp estimates for the Ornstein-Uhlenbeck operator JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze PY - 2004 SP - 447 EP - 480 VL - 3 IS - 3 PB - Scuola Normale Superiore, Pisa UR - http://archive.numdam.org/item/ASNSP_2004_5_3_3_447_0/ LA - en ID - ASNSP_2004_5_3_3_447_0 ER -
%0 Journal Article %A Mauceri, Giancarlo %A Meda, Stefano %A Sjögren, Peter %T Sharp estimates for the Ornstein-Uhlenbeck operator %J Annali della Scuola Normale Superiore di Pisa - Classe di Scienze %D 2004 %P 447-480 %V 3 %N 3 %I Scuola Normale Superiore, Pisa %U http://archive.numdam.org/item/ASNSP_2004_5_3_3_447_0/ %G en %F 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://archive.numdam.org/item/ASNSP_2004_5_3_3_447_0/
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