  We describe the range of a restricted spherical mean transform, which sends a
function supported inside a closed ball in a hyperbolic space to its mean
values on the geodesics spheres centered at the boundary of the ball. The
description resembles that of the same transform on the Euclidean spaces
obtained by Mark Agranovsky, David Finch, and Peter Kuchment [Inverse Problems
and Imaging, 3(3):373--382, 2009] and Mark Agranovsky and Linh V. Nguyen [J.
Anal. Math., 112:351--367, 2010].
  We also derive a similar characterization for the corresponding transform on
the two dimensional spherical space.
