Weighted Strichartz estimates for the Schrödinger and wave equations on Damek–Ricci spaces

Abstract

We prove Strichartz estimates for radial solutions of the Schrodinger and wave equations on Damek–Ricci spaces, and in particular on symmetric spaces of noncompact type and rank one, using the perturbative theory with potentials. The curvature of the noncompact manifold has an influence on the dispersive properties, and indeed we obtain Strichartz estimates with weights at spatial infinity, which are stronger than the standard ones in the flat case.