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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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