Abstract

We consider a class of second order ultraparabolic differential equations with measurable coefficients, that are obtained as a perturbation of hypoelliptic operators. We assume that the hypoelliptic operators have the form of a sum of squares of vector fields plus a drif term and that the vector fields are invariant with respec to a suitalbe homogeneous Lie group structure. We adapt the Moser's iterative methods to the non-Euclidean geometry of the Lie groups and we prove a pointwise bound of the solution u in terms of its norm in the L^p space.