Description of the smoothing effects of semigroups generated by fractional Ornstein–Uhlenbeck operators and subelliptic estimates

We study semigroups generated by general fractional Ornstein–Uhlenbeck operators acting on $$L^2({\mathbb {R}}^n)$$ . characterize geometrically the partial Gevrey-type smoothing properties of these semigroups, and we sharply describe blow-up associated seminorms for short times, generalizing hypoelliptic quadratic cases. As a byproduct this study, establish subelliptic estimates enjoyed whole space using interpolation theory.