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Sharp estimates for the Ornstein-Uhlenbeck operator.

Giancarlo Mauceri ; Stefano Meda ; Peter Sjögren (Institutionen för matematik)
Ann. Scuola Norm. Sup. Pisa Cl. Sci. (5) Vol. III (2006), p. 447--480.
[Artikel, refereegranskad vetenskaplig]

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(zb)| < 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.

Nyckelord: Ornstein--Uhlenbeck operator, functional calculus, spectral multiplier



Denna post skapades 2007-10-18. Senast ändrad 2014-09-29.
CPL Pubid: 55069

 

Institutioner (Chalmers)

Institutionen för matematik (2002-2004)

Ämnesområden

Matematik

Chalmers infrastruktur