WEIGHTED LIPSCHITZ CONTINUITY, SCHWARZ–PICK'S LEMMA AND LANDAU–BLOCH'S THEOREM FOR HYPERBOLIC-HARMONIC MAPPINGS IN ℂN-Reference-Cited by-同舟云学术

WEIGHTED LIPSCHITZ CONTINUITY, SCHWARZ–PICK'S LEMMA AND LANDAU–BLOCH'S THEOREM FOR HYPERBOLIC-HARMONIC MAPPINGS IN ℂN

Published:2013-02-01 Issue:1 Volume:18 Page:66-79
ISSN:1392-6292
Container-title:Mathematical Modelling and Analysis
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Author:

Chen Shaolin¹,Ponnusamy Saminathan²,Wang Xiantao³

Affiliation:

1. Hengyang Normal University Hengyang, 421008 Hunan, China; Hunan Normal University Changsha, 410081 Hunan, China

2. Indian Institute of Technology Madras 600 036 Chennai, India; Indian Statistical Institute (ISI), Chennai Center CIT Campus, Taramani, 600 113 Chennai, India

3. Hunan Normal University Changsha, 410081 Hunan, China; Ministry of Education of China Changsha, Hunan, China

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.

Publisher

Vilnius Gediminas Technical University

Subject

Modeling and Simulation,Analysis

Reference26 articles.

1. Lipschitz-type spaces and harmonic mappings in the space

2. Bloch’s theorem for real variables

3. A Schwarz Lemma for harmonic and hyperbolic-harmonic functions in higher dimensions

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