On Bergman-Orlicz and Campanato-Orlicz spaces of hyperbolic harmonic functions on the real unit ball

Let Phi be a growth function. In this paper, we characterize Bergman-Orlicz spaces $ \mathcal {B}_{\alpha }<^>\Phi $ B alpha Phi of hyperbolic harmonic functions on the real unit ball $ {\mathbb B} $ B in terms of invariant gradients and some integral functions. As an application, several characterizations of h-harmonic Campanato-Orlicz spaces are established. This is a continuous work of [X. Fu and Q. Shi. Complex Var. Elliptic Equ. 2023].