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

Abstract

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.