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

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.