Strichartz estimates for second order hyperbolic operators with nonsmooth coefficients III

In an earlier work of the author it was proved that the Strichartz estimates for second order hyperbolic operators hold in full if the coefficients are of class C 2 C^2 . Here we strengthen this and show that the same holds if the coefficients have two derivatives in L 1 ( L ∞ ) L^1(L^∞ ) . Then we use this result to improve the local theory for second order nonlinear hyperbolic equations.