Scientific Papers

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
\(R_{\alpha}(\rho)(g) =\int_{\mathbb{G}}N(g^{-1}g')^{\alpha-Q}\rho(g')dg'\)
of a nonnegative function \(\rho \in C_0(\mathbb{G})\) on a group \(\mathbb{G}\) of Heisenberg type is necessarily either p-subharmonic or p-superharmonic, depending on p and α. 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.