Optimal dispersive estimates for the wave equation with $C^{(n-3)/2}$ potentials in dimensions $4\le n\le 7$

Abstract

We prove optimal dispersive estimates for the wave group $e^{it\sqrt{-\Delta +V}}$ for a class of real-valued potentials $V\in C^{(n-3)/2}({\mathbf{R}}^n)$, $4\le n\le 7$, such that ${\partial }_x^{\alpha }V(x)=O(|x{|}^{-\delta })$ for $|x|>1$, where $\delta >(n+1)/2$.

34 pages; another appendix is added; some changes are made in the proof in the even dimensional case