Characterization by Asymptotic Mean Formulas of q-Harmonic Functions in Carnot Groups

摘要

Aim of this paper is to extend the work (Ferrari et al. in Discrete Contin. Dyn. Syst. 34, 2779-2793, 2014) to the Carnot group setting. More precisely, we prove that in every Carnot group a function is q-harmonic (here 1 < q < a), if and only if it satisfies a particular asymptotic mean value formula.