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

    Shaolin Chen Affiliation
    ; Saminathan Ponnusamy Affiliation
    ; Xiantao Wang Affiliation

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.

Keyword : hyperbolic-harmonic function, Bloch space, Landau–Bloch's theorem, Schwarz–Pick's lemma

How to Cite
Chen, S., Ponnusamy, S., & Wang, X. (2013). Weighted lipschitz continuity, Schwarz–Pick’s lemma and Landau–Bloch’s theorem for hyperbolic-harmonic mappings in ℂn. Mathematical Modelling and Analysis, 18(1), 66-79. https://doi.org/10.3846/13926292.2013.756834
Published in Issue
Feb 1, 2013
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