Optimal angle of the holomorphic functional calculus for the Ornstein-Uhlenbeck operator

We give a simple proof of the fact that the classical Ornstein-Uhlenbeck operator L is R-sectorial of angle arcsin vertical bar 1 - 2/p vertical bar on L-P(R-d, mu) for I < p < infinity, where mu is the standard Gaussian measure with density d mu = (2 pi)(-d/2) exp(-vertical bar x vertical bar(2)/2)dx. Applying the abstract holomorphic functional calculus theory of Kalton and Weis, this immediately gives a new proof of the fact that L has a bounded H-infinity functional calculus with this optimal angle. Crown Copyright (C) 2019 Published by Elsevier B.V. on behalf of Royal Dutch Mathematical Society (KWG). All rights reserved.