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

Authors:	Chiara Cinti Ermanno Lanconelli

Institution:	(1) Dipartimento di Matematica, Università degli Studi di Bologna, Piazza di Porta S. Donato, 5, 40126 Bologna, Italy

Abstract:	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 $\mathcal{L}$ on a homogeneous Lie group $\mathbb{L}$ . Our results complete the ones obtained in Cinti (Math Scand 100:1–21, 2007). We also provide a suitable theory for $\mathcal{L}$ -Green functions and for $\mathcal{L}$ -Green potentials of Radon measures. The proofs mostly rely on the use of appropriate techniques relevant to the Potential Theory for $\mathcal{L}$ . Investigation supported by University of Bologna. Funds for selected research topics.

Keywords:	H?rmander operators Ultraparabolic operators Potential theory Riesz and Poisson-Jensen representation formulas Green functions and potentials
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