Sharp estimates for the Ornstein-Uhlenbeck operator
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 3 (2004) no. 3, p. 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
@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, Série 5, Tome 3 (2004) no. 3, pp. 447-480. http://www.numdam.org/item/ASNSP_2004_5_3_3_447_0/

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