On smoothing in non autonomous Ornstein-Uhlenbeck equations in infinite dimensions

TL;DR

This paper investigates the smoothing effects of the Ornstein-Uhlenbeck evolution operator in non-autonomous, infinite-dimensional settings and applies these results to establish Schauder estimates for related evolution equations.

Contribution

It provides new smoothing estimates for non-autonomous Ornstein-Uhlenbeck operators in infinite dimensions and uses them to prove Schauder theorems for mild solutions.

Findings

Smoothing properties along specific directions are established for the evolution operator.

Schauder type theorems are proved for solutions of certain evolution equations.

The results extend understanding of regularity in infinite-dimensional stochastic systems.

Abstract

We prove smoothing properties along suitable directions of the Ornstein-Uhlenbeck evolution operator, namely the evolution operator associated to non autonomous Ornstein-Uhlenbeck equations. Moreover we use such smoothing estimates to prove Schauder type theorems, again along suitable directions, for the mild solutions of a class of evolution equations.