Abstract

We consider a class of perturbations of the degenerate Ornstein-Uhlenbeck operator in $\mathbb{R}^N$. Using a revised version of Bernstein’s method we provide several uniform estimates for the semigroup $\lbrace T\rbrace _{t\ge 0}$ associated with the realization of the operator ${\cal A}$ in the space of all the bounded and continuous functions in $\mathbb{R}^N$