Subharmonic functions in sub-Riemannian settings

Abstract

In this note we present mean value characterizations of subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution ¡. These characterizations are based on suitable average operators on the level sets of ¡. Asymptotic characterizations are also considered, extending classical results of Blaschke, Privaloff, Radó, Beckenbach and Reade. The results presented here generalize and carry forward former results of the authors in [6, 8].