Global Morrey estimates for a class of Ornstein-Uhlenbeck operators

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In this paper, we consider a class of hypoelliptic Ornstein-Uhlenbeck operators in ℝ N given by $$\mathcal{A} = \sum\limits_{i,j = 1}^{p_0 } {a_{ij} \partial _{x_i x_j }^2 + } \sum\limits_{i,j = 1}^N {b_{ij} x_i \partial _x } ,$$ where (a ij ), (b ij ) are N × N constant matrices, and (a ij ) is symmetric and positive semidefinite. We deduce global Morrey estimates forA from similar estimates of its evolution operator L on a strip domain S = ℝ N × [−1, 1].