Optimal regularity results in spaces of Hölder continuous functions for some infinite dimensional Ornstein - Uhlenbeck semigroup
In the very interesting paper under review, the author considers the elliptic equation \[ \lambda \varphi - L\varphi = f, \] where \(\lambda > 0,\) \(f\) is \(\theta \)-Hölder continuous and \(L\) is an Ornstein--Uhlenbeck operator over a Hilbert space \(H.\) The main result asserts that the mapping \(D^{2}\varphi\) (with values in the space of Hilbert--Schmidt operators in \(H\)) is \(\theta\)-Hölder continuous.
scientific article; zbMATH DE number 5700399