Strichartz estimates in Wiener amalgam spaces for Schrödinger equations with at most quadratic potentials

Abstract

For Schrödinger equations with potentials which grow at most quadratically at spatial infinity, we prove Strichartz estimates in Wiener amalgam spaces. These estimates provide a stronger recovery of local-in-space regularity than the classical Strichartz estimates in Lebesgue spaces. Our result is a generalization of the results on Strichartz estimates in Wiener amalgam spaces by Cordero and Nicola, which are stated for the potentials $V(x)=0,|x{|}^2/2,-|x{|}^2/2$.

25 pages