Dispersive and Strichartz estimates for the three-dimensional wave equation with a scaling-critical class of potentials

We consider the three-dimensional linear wave equation perturbed by a potential V belonging to a scaling-critical class which is the closure of bounded, compactly supported functions with respect to the global Kato norm. Without any further smallness assumptions, we first prove the dispersive estimate for the solution of the wave equation. As a byproduct, we prove Strichartz estimates under a slightly stronger condition.