  We present sufficient conditions on a smooth uniformly flat hypersurface W in
the unit ball to be an interpolation hypersurface or a sampling hypersurface
for generalized Bergman spaces associated to the unit ball with its Bergman
metric. The conditions are phrased in terms of a geometric Beurling-type
densities, similar to the densities defined for hypersurfaces in C^n by
Ortega-Cerda, Schuster and the second author. For the case of sampling, our
proofs are different than those in the C^n case; we use an approach closer in
spirit to the work of Berndtsson and Ortega-Cerda in the 1-dimensional case.
For the case of interpolation we use a modified version of the Ohsawa-Takegoshi
method to carry out the interpolation in the situation where the density of W
is a little less than optimal. For the general case, we use the same approach
as in the C^n case, except that we use an improved dbar theorem, due to Ohsawa,
to solve our Cousin problem with L^2 bounds. As in the case of C^n, it is
expected that our sufficient conditions are also necessary.
