Weighted Lipschitz continuity, Schwarz-Pick's Lemma and Landau-Bloch's theorem for hyperbolic-harmonic mappings in $\mathbb{C}^{n}$

Abstract

In this paper, we discuss some properties on hyperbolic-harmonic mappings in the unit ball of $\mathbb{C}^{n}$. First, we investigate the relationship between the weighted Lipschitz functions and the hyperbolic-harmonic Bloch spaces. Then we establish the Schwarz-Pick type theorem for hyperbolic-harmonic mappings and apply it to prove the existence of Landau-Bloch constant for mappings in $\alpha$-Bloch spaces.