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We study the Bloch and the little Bloch spaces of harmonic functions on thereal hyperbolic ball. We show that the Bergman projections from$L^\infty(\mathbb B)$ to $\mathcal B$, and from $C_0(\mathbb B)$ to $\mathcalB_0$ are onto. We verify that the dual space of the hyperbolic harmonic Bergmanspace $\mathcal B^1_\alpha$ is $\mathcal B$ and its predual is $\mathcal B_0$.Finally, we obtain an atomic decomposition of Bloch functions as a series ofBergman reproducing kernels.

Harmonic Bloch Space on the Real Hyperbolic Ball