Strichartz estimates in Wiener amalgam spaces for Schrödinger equations with at most quadratic potentials
Shun Takizawa
TL;DR
The paper establishes Strichartz estimates for Schrödinger equations with potentials of at most quadratic growth in Wiener amalgam spaces, improving local regularity recovery compared to classical Lebesgue-space estimates. By combining Hamiltonian flow techniques with short-time Fourier transform methods, the authors decompose the propagator into a parametrix U_0 and a remainder R, proving dispersive-type bounds for both components. They obtain homogeneous, retarded, and endpoint Strichartz estimates in Wiener amalgam spaces, including Lorentz refinements, and discuss global-in-time results in the Stark case. The results generalize prior Wiener amalgam Strichartz results to a broad class of at-most-quadratic potentials and yield well-posedness consequences for perturbed Schrödinger equations in L^2-based settings.
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 $V(x) = 0,|x|^2/2, -|x|^2/2$.