Optimal regularity results in spaces of Hölder continuous functions for some infinite dimensional Ornstein&#8722Uhlenbeck semigroup

Abstract

We consider the elliptic equation λ φ – Lφ = f where λ > 0, f is θ-Hölder continuous and L is an Ornstein−Uhlenbeck operator in a Hilbert space H. We show that the mapping D_2_φ (with values in the space of Hilbert−Schmidt operators on H) is θ-Hölder continuous.