On characterizations of hyperbolic harmonic Bloch and Besov spaces

Document Type : Research Paper


Department of Mathematics‎, ‎Shaoxing University‎, ‎Shaoxing 312000‎, ‎Zhejiang Province‎, ‎P.R‎. ‎China.


‎We define hyperbolic harmonic $\omega$-$\alpha$-Bloch space‎ ‎$\mathcal{B}_\omega^\alpha$ in the unit ball $\mathbb{B}$ of ${\mathbb R}^n$ and‎ ‎characterize it in terms of‎ ‎$$\frac{\omega\big((1-|x|^2)^{\beta}(1-|y|^2)^{\alpha-\beta}\big)|f(x)-f(y)|}{[x,y]^\gamma|x-y|^{1-\gamma}‎},$$ where $0\leq \gamma\leq 1$‎. ‎Similar results are extended to‎ ‎little $\omega$-$\alpha$-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.


Main Subjects

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