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

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

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 func...

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Main Authors: Shaolin Chen, Saminathan Ponnusamy, Xiantao Wang
Format: Article
Language:English
Published: Vilnius Gediminas Technical University 2013-02-01
Series:Mathematical Modelling and Analysis
Subjects:
hyperbolic-harmonic function
Bloch space
Landau–Bloch's theorem
Schwarz–Pick's lemma
Online Access:https://journals.vgtu.lt/index.php/MMA/article/view/4098
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spelling doaj-48f8355be7e84aca99676903924a20b02021-07-02T11:45:53ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102013-02-0118110.3846/13926292.2013.756834Weighted lipschitz continuity, Schwarz–Pick's lemma and Landau–Bloch's theorem for hyperbolic-harmonic mappings in ℂnShaolin Chen0Saminathan Ponnusamy1Xiantao Wang2Hengyang Normal University Hengyang, 421008 Hunan, China; Hunan Normal University Changsha, 410081 Hunan, ChinaIndian Institute of Technology Madras 600 036 Chennai, India; Indian Statistical Institute (ISI), Chennai Center CIT Campus, Taramani, 600 113 Chennai, IndiaHunan Normal University Changsha, 410081 Hunan, China; Ministry of Education of China Changsha, Hunan, China 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. https://journals.vgtu.lt/index.php/MMA/article/view/4098hyperbolic-harmonic functionBloch spaceLandau–Bloch's theoremSchwarz–Pick's lemma
collection DOAJ
language English
format Article
sources DOAJ
author Shaolin Chen
Saminathan Ponnusamy
Xiantao Wang
spellingShingle Shaolin Chen
Saminathan Ponnusamy
Xiantao Wang
Weighted lipschitz continuity, Schwarz–Pick's lemma and Landau–Bloch's theorem for hyperbolic-harmonic mappings in ℂn
Mathematical Modelling and Analysis
hyperbolic-harmonic function
Bloch space
Landau–Bloch's theorem
Schwarz–Pick's lemma
author_facet Shaolin Chen
Saminathan Ponnusamy
Xiantao Wang
author_sort Shaolin Chen
title Weighted lipschitz continuity, Schwarz–Pick's lemma and Landau–Bloch's theorem for hyperbolic-harmonic mappings in ℂn
title_short Weighted lipschitz continuity, Schwarz–Pick's lemma and Landau–Bloch's theorem for hyperbolic-harmonic mappings in ℂn
title_full Weighted lipschitz continuity, Schwarz–Pick's lemma and Landau–Bloch's theorem for hyperbolic-harmonic mappings in ℂn
title_fullStr Weighted lipschitz continuity, Schwarz–Pick's lemma and Landau–Bloch's theorem for hyperbolic-harmonic mappings in ℂn
title_full_unstemmed Weighted lipschitz continuity, Schwarz–Pick's lemma and Landau–Bloch's theorem for hyperbolic-harmonic mappings in ℂn
title_sort weighted lipschitz continuity, schwarz–pick's lemma and landau–bloch's theorem for hyperbolic-harmonic mappings in ℂn
publisher Vilnius Gediminas Technical University
series Mathematical Modelling and Analysis
issn 1392-6292
1648-3510
publishDate 2013-02-01
description 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.
topic hyperbolic-harmonic function
Bloch space
Landau–Bloch's theorem
Schwarz–Pick's lemma
url https://journals.vgtu.lt/index.php/MMA/article/view/4098
work_keys_str_mv AT shaolinchen weightedlipschitzcontinuityschwarzpickslemmaandlandaublochstheoremforhyperbolicharmonicmappingsincn
AT saminathanponnusamy weightedlipschitzcontinuityschwarzpickslemmaandlandaublochstheoremforhyperbolicharmonicmappingsincn
AT xiantaowang weightedlipschitzcontinuityschwarzpickslemmaandlandaublochstheoremforhyperbolicharmonicmappingsincn
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