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

Abstract

Using 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 the range $α>-1$ to all $α\in\mathbb R$. We then generalize several properties of Bergman spaces; projection, duality, atomic decomposition, and inclusion relations, to this extended family.