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

Abstract

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

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Cited by in corpus (2)

• Schauder theorems for a class of (pseudo-)differential operators on finite and infinite dimensional state spaces
• Null-controllability of evolution equations associated with fractional Shubin operators through quantitative Agmon estimates