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

2016/12/20 by Jiaolong Chen, Chen, Jiaolong
Mathematics · #31B05 #31C05 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1612.06542

openalex publication_date 2016/12/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the properties of hyperbolic harmonic mappings in the unit ball \mathbbBⁿ in \IRⁿ (n≥ 2). Firstly, we establish necessary and sufficient conditions for a hyperbolic harmonic mapping to be in the Bloch space B(\mathbbBⁿ) and the generalized Bloch space L_∞,ωB_α,a⁰(\mathbbBⁿ), 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.

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