Riesz-type representation formulas for subharmonic functions in sub-Riemannian settings

Abstract

<p style='text-indent:20px;'>In this paper we use a potential-theoretic approach to establish various representation theorems and Poisson-Jensen-type formulas for subharmonic functions in sub-Riemannian settings. We also characterize the Radon measures in <inline-formula><tex-math id="M1">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula> which are the Riesz-measures of bounded-above subharmonic functions in the whole space <inline-formula><tex-math id="M2">\begin{document}$ \mathbb{R}^N $\end{document}</tex-math></inline-formula>.</p>