Riesz and Poisson-Jensen Representation Formulas for a Class of Ultraparabolic Operators on Lie Groups

摘要

The aim of this paper is to give some representation formulas of Riesz and Poisson-Jensen type for super-solutions to a class of hypoelliptic ultraparabolic operators Lmathcal{L} on a homogeneous Lie group mathbbLmathbb{L}. Our results complete the ones obtained in Cinti (Math Scand 100:1–21, 2007). We also provide a suitable theory for Lmathcal{L}-Green functions and for Lmathcal{L}-Green potentials of Radon measures. The proofs mostly rely on the use of appropriate techniques relevant to the Potential Theory for Lmathcal{L}.