A Poisson-Jensen type representation formula for subharmonic functions on stratified Lie groups
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.
Poisson-Jensen representation formula, stratified Lie groups
scientific article; zbMATH DE number 2162534