  We examine solutions to semilinear wave equations on black hole backgrounds
and give a proof of an analog of the Strauss conjecture on the Schwarzschild
and Kerr, with small angular momentum, black hole backgrounds. The key
estimates are a class of weighted Strichartz estimates, which are used near
infinity where the metrics can be viewed as small perturbations of the
Minkowski metric, and a localized energy estimate on the black hole background,
which handles the behavior in the remaining compact set.
