On local-in-time Strichartz estimates for the Schrödinger equation with singular potentials

Abstract

There have been a lot of works concerning the Strichartz estimates for the perturbed Schrödinger equation by potential. These can be basically carried out adopting the well-known procedure for obtaining the Strichartz estimates from the weighted $L^2$ resolvent estimates for the Laplacian. In this paper we handle the Strichartz estimates without relying on the resolvent estimates. This enables us to consider various potential classes such as the Morrey-Campanato classes.

To appear in Math. Nachr., 9 pages