Subharmonic functions in sub-Riemannian settings

Bonfiglioli, Andrea, and Lanconelli, Ermanno. "Subharmonic functions in sub-Riemannian settings." Journal of the European Mathematical Society 015.2 (2013): 387-441. <http://eudml.org/doc/277194>.

@article{Bonfiglioli2013,
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 $\Gamma $. These characterizations are based on suitable average operators on the level sets of $\Gamma $. 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 weak sense of distributions, and we show how to approximate subharmonic functions by smooth ones. The classes of operators involved are wide enough to comprise, as very special cases, the sub-Laplacians on Carnot groups. The results presented here generalize and carry forward former results of the authors in [6, 8].},
author = {Bonfiglioli, Andrea, Lanconelli, Ermanno},
journal = {Journal of the European Mathematical Society},
keywords = {subharmonic function; mean-integral operator; Carnot group; subharmonic functions; Carnot groups},
language = {eng},
number = {2},
pages = {387-441},
publisher = {European Mathematical Society Publishing House},
title = {Subharmonic functions in sub-Riemannian settings},
url = {http://eudml.org/doc/277194},
volume = {015},
year = {2013},
}

TY - JOUR
AU - Bonfiglioli, Andrea
AU - Lanconelli, Ermanno
TI - Subharmonic functions in sub-Riemannian settings
JO - Journal of the European Mathematical Society
PY - 2013
PB - European Mathematical Society Publishing House
VL - 015
IS - 2
SP - 387
EP - 441
AB - 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 $\Gamma $. These characterizations are based on suitable average operators on the level sets of $\Gamma $. 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 weak sense of distributions, and we show how to approximate subharmonic functions by smooth ones. The classes of operators involved are wide enough to comprise, as very special cases, the sub-Laplacians on Carnot groups. The results presented here generalize and carry forward former results of the authors in [6, 8].
LA - eng
KW - subharmonic function; mean-integral operator; Carnot group; subharmonic functions; Carnot groups
UR - http://eudml.org/doc/277194
ER -