Harmonic Bergman Spaces on the Real Hyperbolic Ball: Atomic Decomposition, Interpolation and Inclusion Relations

For alpha > -1 and 0 < p < infinity, we study weighted Bergman spaces B-alpha(p) of harmonic functions on the real hyperbolic ball. We obtain an atomic decomposition of Bergman functions in terms of reproducing kernels. We show that an r-separated sequence {a(m)} with sufficiently larger is an interpolating sequence for B-alpha(p). Using these we determine precisely when a Bergman space B-alpha(p) is included in another Bergman space B-beta(q).