A boundary estimate for non-negative solutions to Kolmogorov operators in non-divergence form

We consider non-negative solutions to a class of second-order degenerate Kolmogorov operators of the form where z = ( x , t ) belongs to an open set , and 1 ≤ m ≤ N . Let , let K be a compact subset of , and let be such that . We give sufficient geometric conditions for the validity of the following Carleson type estimate. There exists a positive constant C K , depending only on and on , such that for every non-negative solution u of in Ω such that .