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Sharp estimates for the Ornstein-Uhlenbeck operator. (English) Zbl 1116.47036
The purpose of this paper is to obtain a sharp functional calculus for the Ornstein-Uhlenbeck operator $$T$$ acting on the $$L^p$$ spaces with respect to the Gaussian measure $$\gamma$$ on $$\mathbb R^d$$. The authors prove a sharp estimate of the operator norm of the imaginary powers of $$T$$ on $$L^p(\gamma), \quad 1<p<+\infty$$. This result improves earlier results of the authors with J. Garcia-Cuerva and J. L. Torrea.

##### MSC:
 47D06 One-parameter semigroups and linear evolution equations 47A60 Functional calculus for linear operators 47N30 Applications of operator theory in probability theory and statistics 60G15 Gaussian processes
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##### References:
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