Low-frequency dispersive estimates for the wave equation in higher dimensions

We prove dispersive estimates at low frequency in dimensions n≥4 for the wave equation for a very large class of real-valued potentials, provided zero is neither an eigenvalue nor a resonance. This class includes potentials V∈L^∞(Rⁿ) satisfying V(x)=O(〈x〉^{−(n+1)/2−ε}), ε>0.