Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term

Abstract

We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type $$ \mathcal {L}_0 u + \mathcal {V} u = 0, $$ where $\mathcal {L}_0$ is a linear second order hypoelliptic operator and $\mathcal {V}$ belongs to a class of functions of Stummel-Kato type. We also obtain the existence of a Green function and an uniqueness result for the Cauchy-Dirichlet problem.