In this paper we furnish mean value characterizations for subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution 0. These characterizations are based on suitable average operators on the level sets of 0. Asymptotic characterizations are also considered, extending classical results of Blaschke, Privaloff, Radó, Beckenbach, Reade and Saks.We analyze as well the notion of subharmonic function in the sense of distributions, and we show how to approximate subharmonic functions by smooth ones. The classes of operators involved are wide enough to contain, as very special cases, the sub-Laplacians on Carnot groups. The results presented here generalize and carry forward former results of the authors.
Subharmonic functions in sub-Riemannian settings
BONFIGLIOLI, ANDREA;LANCONELLI, ERMANNO
2013
Abstract
In this paper we furnish mean value characterizations for subharmonic functions related to linear second order partial differential operators with nonnegative characteristic form, possessing a well-behaved fundamental solution 0. These characterizations are based on suitable average operators on the level sets of 0. Asymptotic characterizations are also considered, extending classical results of Blaschke, Privaloff, Radó, Beckenbach, Reade and Saks.We analyze as well the notion of subharmonic function in the sense of distributions, and we show how to approximate subharmonic functions by smooth ones. The classes of operators involved are wide enough to contain, as very special cases, the sub-Laplacians on Carnot groups. The results presented here generalize and carry forward former results of the authors.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
