L p -regularity for parabolic operators with unbounded time-dependent coefficients

Abstract

We establish the maximal regularity for nonautonomous Ornstein–Uhlenbeck operators in L p-spaces with respect to a family of invariant measures, where \({p \in (1, +\infty)}\) . This result follows from the maximal L p-regularity for a class of elliptic operators with unbounded, time-dependent drift coefficients and potentials acting on \({L^{p}(\mathbb{R}^{N} )}\) with Lebesgue measure.