Generalized Bloch spaces, integral means of hyperbolic harmonic mappings in the unit ball

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Chen, Jiaolong¹ 

[1] Hunan Normal Univ, Key Lab High Performance Comp & Stochast Informat, Minist Educ China, Coll Math & Stat, Changsha 410081, Hunan, Peoples R China

关键词: Hyperbolic harmonic mapping;    Generalized Bloch space;    Integral means;    Weak uniform boundedness property;   

DOI  :  10.1016/j.jmaa.2018.04.023

来源: Elsevier

【 摘 要 】

In this paper, we investigate the properties of hyperbolic harmonic mappings in the unit ball B-n in R-n (n >= 2). Firstly, we establish necessary and sufficient conditions for a hyperbolic harmonic mapping to be in the Bloch space B(B-n) and the generalized Bloch space L infinity,omega B alpha,a0(B-n), respectively. Secondly, we discuss the relationship between the integral means of hyperbolic harmonic mappings and that of their gradients. The obtained results are the generalizations of Hardy and Littlewood's related ones in the setting of hyperbolic harmonic mappings. Finally, we characterize the weak uniform boundedness property of hyperbolic harmonic mappings in terms of the quasihyperbolic metric. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

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