Hardy-Sobolev type estimates on certain Riemannian manifolds and Lie groups (Q1207144)

The author proves two fundamental results. The first result (Theorem I) gives potential estimates on a connected and simple connected Riemannian manifold \(M\) with nonpositive curvature (a Cartan-Hadamard manifold). In this case the measure considered on \(M\) is the measure induced by the Riemannian structure of \(M\). The second result (Theorem II) gives potential estimates on a nilpotent and simple connected Lie group on which is considered the left-invariant Haar measure.