Bounded holomorphic functional calculus for nonsymmetric Ornstein-Uhlenbeck operators

We study bounded holomorphic functional calculus for nonsymmetric infinite dimensional Ornstein-Uhlenbeck operators L. We prove that if -L generates an analytic semigroup on L-2(gamma infinity), then L has bounded holomorphic functional calculus on L-r(gamma infinity), 1 < r < infinity, in any sector of angle u > u(r)*, where gamma infinity is the associated invariant measure and u(r)* the sectoriality angle of L on L-r(gamma infinity). The angle u(r)* is optimal. In particular our result applies to any non-degenerate finite dimensional Ornstein-Uhlenbeck operator, with dimension-free estimates.