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 funct...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2013-02-01
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| Series: | Mathematical Modelling and Analysis |
| Subjects: | |
| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/4098 |
| _version_ | 1818566142909743104 |
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| author | Shaolin Chen Saminathan Ponnusamy Xiantao Wang |
| author_facet | Shaolin Chen Saminathan Ponnusamy Xiantao Wang |
| author_sort | Shaolin Chen |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-14T01:49:58Z |
| format | Article |
| id | doaj.art-48f8355be7e84aca99676903924a20b0 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-14T01:49:58Z |
| publishDate | 2013-02-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-48f8355be7e84aca99676903924a20b02022-12-21T23:21:25ZengVilnius 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, ChinaIn 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 |
| 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 |
| title | 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_short | 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 |
| 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 |
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