Weighted Lipschitz Continuity, Schwarz–Pick's Lemma and Landau–Bloch's Theorem for Hyperbolic-Harmonic Mappings in ℂ n
Weighted Lipschitz Continuity, Schwarz–Pick's Lemma and Landau–Bloch's Theorem for Hyperbolic-Harmonic Mappings in ℂ n
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DOI：
10.3846/13926292.2013.756834
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发表时间：
2013-01
影响因子：
1.8
通讯作者：
Shaolin Chen;S. Ponnusamy;Xiantao Wang
中科院分区：
文献类型：
--
作者：
Shaolin Chen;S. Ponnusamy;Xiantao Wang
摘要 本文讨论了 ℂ n 单位球中双曲调和函数的一些性质。首先，我们研究加权 Lipschitz 函数与双曲调和 Bloch 空间之间的关系。然后我们建立了双曲调和函数的Schwarz-Pick型定理，并应用它证明了α-Bloch空间中函数的Landau-Bloch常数的存在性。
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.