This paper establishes new estimates for linear Schroedinger equations in 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.
Beceanu, Marius, "New Estimates for a Time-Dependent Schroedinger Equation" (2009). Mathematics and Statistics Faculty Scholarship. 17.