We prove that a probability solution of the stationary Kolmogorov equation generated by first order perturbation v Ornstein–Uhlenbeck operator L possesses highly integrable density with respect to Gaussian measure satisfying non-perturbed provided is sufficiently integrable. More generally, similar estimate proved for solutions inequalities connected Markov semigroup generators under curvature ...

We establish spatial a priori estimates for the solution u to class of dilation invariant Kolmogorov equation, where is assumed only have certain amount regularity in diffusion’s directions, i.e. $$x_{1}, \ldots , x_{m_{0}}$$ . The result that also regular with respect remaining directions. approach we propose based on commutators identities and allows us obtain Sobolev exponent does not depend...