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Subharmonic functions on Carnot groups. (English) Zbl 1017.31003
The authors develop a potential theory for $$\Delta_G$$-subharmonic functions in $$\mathbb{R}^N$$, where $$\Delta_G$$ is the sub-Laplacian in a Carnot group $$G$$. The main results are analogues to Riesz representation and Poisson-Jensen formulas, Nevanlinna type theorems, and a characterization of the $$\Delta_G$$-Riesz measures of upper bounded $$\Delta_G$$-subharmonic functions on the whole $$\mathbb{R}^N$$.

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