Weighted lipschitz continuity, Schwarz–Pick's lemma and Landau–Bloch's theorem for hyperbolic-harmonic mappings in ℂn

Abstract

In this paper, we discuss some properties on hyperbolic-harmonic functions in the unit ball of 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 functions and apply it to prove the existence of Landau-Bloch constant for functions in α-Bloch spaces.