فضاهای بالک متمرکز شده، ابزار انتگرال طبقه بندی هارمونیک هذلولی در توپ واحد است

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