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Functional calculus for some perturbations of the Ornstein-Uhlenbeck operator
Abstract:
In a recent paper Garc{\'i}a--Cuerva, Mauceri, Meda, Sj\"ogren and Torrea have shown that for every $p$ in $(1,\infty)$ the symmetric finite dimensional \OU operator $\cL^{ou}=-\smallfrac{1}{2}\Delta +x\cdot\nabla$ has a bounded holomorphic functional calculus on $L^p$ in the sector of angle $\phi^*_p=\arcsin|1-2/p|.$ We prove a similar result for some perturbations of the \OU operator.

Keywords:
Ornstein-Uhlenbeck operator, interpolation, functional calculus, spectral multiplier

MSC:
47, 42, 60

Pubblicato su: Mathematische Zeitschrift Vol. 262 (2009) N. 2 Pag. 313-347