Global Morrey estimates for a class of Ornstein-Uhlenbeck operators

In this paper, we consider a class of hypoelliptic Ornstein-Uhlenbeck operators in ℝN given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{A} = \sum\limits_{i,j = 1}^{p_0 } {a_{ij} \partial _{x_i x_j }^2 + } \sum\limits_{i,j = 1}^N {b_{ij} x_i \partial _x } ,$\end{document} where (aij), (bij) are N × N constant matrices, and (aij) is symmetric and positive semidefinite. We deduce global Morrey estimates forA from similar estimates of its evolution operator L on a strip domain S = ℝN × [−1, 1].