  We~describe a Dirichlet-type space of $H$-harmonic functions, i.e. functions
annihilated by the hyperbolic Laplacian on~the unit ball of the real $n$-space,
as~the analytic continuation (in~the spirit of Rossi and Vergne) of the
corresponding weighted Bergman spaces. Characterizations in terms of
derivatives are given, and the associated semi-inner product is shown to be
Moebius invariant. We~also give a formula for the corresponding reproducing
kernel. Our~results solve an open problem addressed by M.~Stoll in his book
``Harmonic and subharmonic function theory on the hyperbolic ball'' (Cambridge
University Press, 2016).
