Sharp Strichartz inequalities in low dimensions

Dirk Hundertmark University of Illinois at Urbana-Champaign, USA

We give a short proof of the Strichartz inequality for the free Schrödinger evolution in dimension one and two. The Strichartz inequality bounds a certain spacetime L^{p}-norm of the solution in terms of the L^{2}-norm of the initial conditions. Basically, the sharp inequality follows from the innocent looking fact that a projection operarator is bounded by the identity. As a byproduct, we also get a simple criterion for the extremizers, which implies that the extremizers are given by Gaussians. This is joint work with Vadim Zharnitsky, UIUC.