An Invariant Harnack Inequality for a Class of Hypoelliptic Ultraparabolic Equations

We show an invariant Harnack inequality for a class of hypoelliptic ultraparabolic operators with underlying homogeneous Lie group structures. As a byproduct we prove a Liouville type theorem for the related “stationary” operators. We also introduce a notion of link of homogeneous Lie Groups that allows us to show that our results apply to wide classes of operators