  We prove estimates for solutions of the Cauchy problem for the inhomogeneous
wave equation on $\R^{1+n}$ in a class of Banach spaces whose norms only depend
on the size of the space-time Fourier transform. The estimates are local in
time, and this allows one, essentially, to replace the symbol of the wave
operator, which vanishes on the light cone in Fourier space, with an
inhomogeneous symbol, which can be inverted. Our result improves earlier
estimates of this type proved by Klainerman-Machedon. As a corollary, one
obtains a rather general result concerning local well-posedness of nonlinear
wave equations.
