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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.

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
Full Text: EuDML
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