Open AccessRiesz-type representation formulas for subharmonic functions in sub-Riemannian settings
Author(s) -
Beatrice Abbondanza,
Stefano Biagi
Publication year - 2021
Publication title -
communications on pure and applied analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.077
H-Index - 42
eISSN - 1553-5258
pISSN - 1534-0392
DOI - 10.3934/cpaa.2021101
Subject(s) - subharmonic , mathematics , bounded function , type (biology) , representation (politics) , space (punctuation) , subharmonic function , pure mathematics , mathematical analysis , physics , linguistics , ecology , philosophy , quantum mechanics , nonlinear system , politics , political science , law , biology
In this paper we use a potential-theoretic approach to establish various representation theorems and Poisson-Jensen-type formulas for subharmonic functions in sub-Riemannian settings. We also characterize the Radon measures in \begin{document}$ \mathbb{R}^N $\end{document} which are the Riesz-measures of bounded-above subharmonic functions in the whole space \begin{document}$ \mathbb{R}^N $\end{document} .