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Subharmonic functions in sub-Riemannian settings. (English) Zbl 1270.31002
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.

MSC:
31C05 Harmonic, subharmonic, superharmonic functions on other spaces
35H20 Subelliptic equations
35J70 Degenerate elliptic equations
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