Abstract
The aim of this paper is to prove a representation formula of Poisson–Jensen type on bounded domains Ω for subharmonic functions related to sub-Laplacians ΔG on stratified Lie groups G. Our result gives a complete answer to a question arisen in Math. Ann. 325 (2003), 97–122, where the additional hypothesis that Ω is regular for the Dirichlet problem related to ΔG was made: here we treat the case of arbitrary bounded domains Ω, omitting the hypothesis of regularity. In order to prove our representation formula, an ad-hoc theory of polar sets and capacity with respect to ΔG is also provided.
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