We prove a Harnack inequality for the positive solutions of ultraparabolic equations of the type L_0 u + V u = 0, where L_0 is a linear second order hypoelliptic operator and 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.
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Polidoro et al. (2008) studied this question.