$\mathcal H$-Harmonic Bergman-Besov Spaces on the Real Hyperbolic Ball

Using the characterizations in terms of various differential operators including partial, normal, and tangential derivatives, we extend the family of Bergman spaces of $\mathcal H$-harmonic functions on the real hyperbolic ball from $\alpha>-1$ to all $\alpha\in\mathbb R$. We then generalize several properties of Bergman spaces such as projection, duality, and inclusion relations, to this extended family.