  For $\alpha>-1$ and $0<p<\infty$, we study weighted Bergman spaces $\mathcal
B^p_\alpha$ of harmonic functions on the real hyperbolic ball and obtain an
atomic decomposition of these spaces in terms of reproducing kernels. We show
that an $r$-separated sequence $\{a_m\}$ with sufficiently large $r$ is an
interpolating sequence for $\mathcal B^p_\alpha$. Using these we determine
precisely when a Bergman space $\mathcal B^p_\alpha$ is included in another
Bergman space $\mathcal B^q_\beta$.
