Poisson process and sharp constants in $L^p$ and Schauder estimates for a class of degenerate Kolmogorov operators

Abstract

We consider a possibly degenerate Kolmogorov Ornstein–Uhlenbeck operator of the form $L={\rm Tr}(BD^2)+\langle Az,D\rangle $, where $A$, $B $ are $N\times N $ matrices, $z \in \mathbb R^N$, $N\ge 1 $, which satisfy the Kalman condition which is equivalent