Abstract
In a recent paper García-Cuerva et al. have shown that for every p in (1,∞) the symmetric finite-dimensional Ornstein–Uhlenbeck operator \({\mathcal{L}^{ou} = -\frac{1}{2}\Delta + x \cdot \nabla}\) 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 Ornstein–Uhlenbeck operator.
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Work partially supported by the Progetto Cofinanziato MIUR “Analisi Armonica” and the Gruppo Nazionale INdAM per l’Analisi Matematica, la Probabilitàe le loro Applicazioni.
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Carbonaro, A. Functional calculus for some perturbations of the Ornstein–Uhlenbeck operator. Math. Z. 262, 313–347 (2009). https://doi.org/10.1007/s00209-008-0375-9
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DOI: https://doi.org/10.1007/s00209-008-0375-9