Subharmonic functions in sub-Riemannian settings (Q1940818)

The authors give the mean value as well as the asymptotic characterization for \(\mathcal L\)-subharmonic functions, where \(\mathcal L\) is a second order differential operator with non-negative characteristic form and well-behaved fundamental solution. An example of \(\mathcal L\) can be the sub-Laplacian on Carnot groups. The authors also show how to approximate a subharmonic (in the sense of distributions) function by a smooth one.