A Note on the Computation of Green Functions for Sublaplacians on Lie Algebras of Type H

In [4] A. Kaplan introduced a class of step-2 nilpotent Lie groups for which the fundamental solution corresponding to the standard sublaplacian may be written down in an explicit elementary form. He also says that heuristic evidence suggests that these groups are the only ones which admit such nice explicit formulas. When I tried to convince myself of this evidence I found some modifications of Kaplan’s proof, which give additional insight into the problem and may be — at least for people working in potential theory — regarded as a simplification.