Riesz potentials and p-superharmonic functions in Lie groups of Heisenberg type

We prove a superposition principle for Riesz potentials of nonnegative continuous functions on Lie groups of Heisenberg type. More precisely, we show that the Riesz potential R _α(ρ)(g)=∫ _GN(g ^-1g') ^α-Qρ(g')dg' of a nonnegative function C0() on a group of Heisenberg type is necessarily either p-subharmonic or p-superharmonic, depending on p and. Here N denotes the anisotropic homogeneous norm on such groups introduced by Kaplan. This result extends to a wide class of nonabelian stratified Lie groups a recent remarkable superposition result of Crandall and Zhang.