Lipschitz type characterizations for Bergman-Orlicz spaces of eigenfunctions on hyperbolic space

We characterize Bergman-Orlicz spaces of eigenfunctions on hyperbolic space in terms of Lipschitz type conditions with respect to pseudo-hyperbolic, hyperbolic and Euclidean metrics. As an application, some properties of symmetric lifting operators defined by the difference quotients of eigenfunctions are obatined. Our results of this paper are extensions of the corresponding known ones in classical weighted Bergman spaces.