Sharp estimates for the Ornstein-Uhlenbeck operator.
Journal article, 2006

Let L be the Ornstein-Uhlenbeck operator which is self-adjoint with respect to the Gauss measure γ on Rd. We prove a sharp estimate of the operator norm of the imaginary powers of L on Lp(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 ∈ C : |arg(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(L) is bounded on Lp(γ). This improves earlier results of the authors with J. García-Cuerva and J.L. Torrea.

functional calculus

spectral multiplier

Ornstein--Uhlenbeck operator


Giancarlo Mauceri

University of Genoa

Stefano Meda

University of Milano-Bicocca

Peter Sjögren

University of Gothenburg

Chalmers, Mathematical Sciences

Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5)

Vol. III 447--480-

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