Harmonic Bloch space on the real hyperbolic ball

We study the Bloch and the little Bloch spaces of harmonic functions on the real hyperbolic ball. We show that the Bergman projections from L^∞ (B) L ∞ ( B ) to B B , and from C₀(B) C 0 ( B ) to B₀ B 0 are onto. We verify that the dual space of the hyperbolic harmonic Bergman space B¹_α B α 1 is B B and its predual is B₀ B 0 . Finally, we obtain atomic decompositions of Bloch functions as series of Bergman reproducing kernels.