$$\alpha $$α-Bloch Mappings on Bounded Symmetric Domains in $${\mathbb {C}}^n$$Cn
$$\alpha $$α-Bloch Mappings on Bounded Symmetric Domains in $${\mathbb {C}}^n$$Cn
复制标题
$${mathbb {C}}^n$$Cn 有界对称域上的 $$alpha $$α-Bloch 映射
DOI：
10.1007/s11785-017-0718-9
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发表时间：
2018
影响因子：
0.8
通讯作者：
G. Kohr
中科院分区：
文献类型：
--
作者：
H. Hamada;G. Kohr
设$${\mathbb{B}}_X$$bX是有限维JB*-三元组$$X=({\mathbb{C}}^n，\vert\cot\vert_X)$$X=(Cn，‖·‖X)的开单位球的有界对称域.本文给出了单位圆盘上$$\Alpha$$α-Bloch映射的定义，它是单位圆盘上$$\Alpha$$α-Bloch函数在$$\Mathbb{C}$$C中的推广。我们将Bonk的偏差定理推广到$$\α$$α-Bloch映射在$${Mathbb{B}}_X$$BX上。作为应用，我们给出了$${\mathbb{B}}_X$$BX上$$\α$$α-Bloch映射的Bloch常数的下界。
Let $${\mathbb {B}}_X$$BX be a bounded symmetric domain realized as the open unit ball of a finite dimensional JB*-triple $$X=({\mathbb {C}}^n, \Vert \cdot \Vert _X)$$X=(Cn,‖·‖X). In this paper, we give a definition of $$\alpha $$α-Bloch mappings on $${\mathbb {B}}_X$$BX which is a generalization of $$\alpha $$α-Bloch functions on the unit disc in $${\mathbb {C}}$$C. This definition is new in the case of the Euclidean unit ball $${\mathbb {B}}^n$$Bn in $${\mathbb {C}}^n$$Cn. We generalize Bonk’s distortion theorem to $$\alpha $$α-Bloch mappings on $${\mathbb {B}}_X$$BX. As an application, we give a lower bound of the Bloch constant for $$\alpha $$α-Bloch mappings on $${\mathbb {B}}_X$$BX.