Abstract

Let ${\mathcal{L}}$ be a sub-laplacian on a stratified Lie group ${G}$. In this paper we study the Dirichlet problem for ${\mathcal{L}}$ with $L^p$-boundary data, on domains $\Omega $ which are contractible with respect to the natural dilations of ${G}$. One of the main difficulties we face is the presence of non-regular boundary points for the usual Dirichlet problem for ${\mathcal{L}}$. A potential theory approach is followed. The main results are applied to study a suitable notion of Hardy spaces