A Poisson-Jensen type representation formula for subharmonic functions on stratified Lie groups
type: Item
instance of: scholarly article
title: A Poisson-Jensen type representation formula for subharmonic functions on stratified Lie groups
zbMATH Open document ID: 1069.31001
author: Andrea Bonfiglioli
author: Chiara Cinti
published in: Potential Analysis
publication date: 2005-04-29T00:00:00Z
review text: The paper deals with a representation formula of Poisson-Jensen type on bounded domains for subharmonic functions related to sub-Laplacians \(\Delta_{\mathbb G}\) on stratified Lie groups \({\mathbb G}\) \[ u(x)=\int_{\partial_1\Omega}u(y)\,d\bar\mu^\Omega_x(y) - \int_{\Omega\cup\partial_2\Omega}\overline G_\Omega(y,x)\,d\mu_u(y) \] in an arbitrary bounded domain \(\Omega\subset{\mathbb G}.\) The proof is based on an ad-hoc theory of polar sets in relation to \(\Delta_{\mathbb G}\)-capacity and the problem of Dirichlet.
Mathematics Subject Classification ID: 31B10
Mathematics Subject Classification ID: 31C05
Mathematics Subject Classification ID: 31B15
Mathematics Subject Classification ID: 35J70
Mathematics Subject Classification ID: 43A80
zbMATH DE Number: 2162534
zbMATH Keywords: Poisson-Jensen representation formula, stratified Lie groups
zbMATH Keywords: sub-Laplacians, subharmonic functions
zbMATH Keywords: capacity
zbMATH Keywords: polar sets.
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: s11118-004-0588-4
OpenAlex ID: W2082499943
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Wikidata QID: Q115381455
DOI: 10.1007/S11118-004-0588-4
description: scientific article; zbMATH DE number 2162534