Uniform decay of local energy and the semi-linear wave equation on Schwarzschild space

We provide a uniform decay estimate for the local energy of general solutions to the inhomogeneous wave equation on a Schwarzschild background. Our estimate implies that such solutions have asymptotic behavior |phi| = O(r(-1)\t - | r *|\(-1/2)) as long as the source term is bounded in the norm (1- 2M/r)(-1).(1+ t +| r *|)L--1(1)(H-Omega(3)(r(2)dr* d omega)). In particular this gives scattering at small amplitudes for non-linear scalar fields of the form square(g)phi =lambda|phi|(p)phi for all 2 < p.