Strichartz Estimates and Maximal Operators for the Wave Equation in R^3

Abstract

We prove sharp Strichartz-type estimates in three dimensions, including some which hold in reverse spacetime norms, for the wave equation with potential. These results are also tied to maximal operator estimates studied by Rogers--Villaroya, of which we prove a sharper version. As a sample application, we use these results to prove the local well-posedness and the global well-posedness for small initial data of semilinear wave equations in R^3 with quintic or higher monomial nonlinearities.