On characterizations of hyperbolic harmonic Bloch and Besov spaces

We define hyperbolic harmonic ω-α-Bloch space‎ ‎B^αω in the unit ball B of Rn and‎ ‎characterize it in terms of‎ ‎ ω((1−|x|2)β(1−|y|2)α−β)|f(x)−f(y)|[x,y]γ|x−y|1−γ‎, where 0≤γ≤1‎. ‎Similar results are extended to‎ ‎little ω-α-Bloch and Besov spaces‎. ‎These obtained‎ ‎characterizations generalize the corresponding ones which were obtained by G‎. ‎Ren‎ ‎and U‎. ‎K\ {a}hler in 2002 and 2005‎.