New estimates for a time-dependent Schrödinger equation

Abstract

This paper establishes new estimates for linear Schrödinger equations in ${\mathbb{R}}^3$ with time-dependent potentials. Some of the results are new even in the time-independent case, and all are shown to hold for potentials in scaling-critical, translation-invariant spaces. The proof of the time-independent results uses a novel method based on an abstract version of Wiener's theorem.