Smoothing Properties of Fractional Ornstein-Uhlenbeck Semigroups and\n Null-Controllability

Abstract

We study fractional hypoelliptic Ornstein-Uhlenbeck operators acting on\n$L^2(\\mathbb{R}^n)$ satisfying the Kalman rank condition. We prove that the\nsemigroups generated by these operators enjoy Gevrey regularizing effects. Two\nbyproducts are derived from this smoothing property. On the one hand, we prove\nthe null-controllability in any positive time from thick control subsets of the\nassociated parabolic equations posed on the whole space. On the other hand, by\nusing interpolation theory, we get global $L^2$ subelliptic estimates for the\nthese operators.\n