Extremal problems of Bloch function spaces期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

Extremal problems of Bloch function spaces

Authors:	Zhang Shunyan Wang Wei

Affiliation:	(1) Department of Mathematics, Peking University, 100871 Beijing, China

Abstract:	Letf be analytic in a hyperbolic region . The Bloch constant_f off is defined by $beta _f = mathop {sup }limits_{z in Omega } \|f'(z)\|/lambda _Omega (z)$ , where (z)\|dz\| is the Poincaré metric in . Suppose is hyperbolic and $mathop {lim inf }limits_{omega to c} lambda _Delta (w) > lambda (Delta ) > 0,forall c in partial Delta$ where $lambda (Delta ) = mathop {inf}limits_{w in Delta } lambda _Delta (w)$ . Then for allf withf() , we have_f 1/(). In this paper we study the extremal functions defined by_f=1/() and the existence of those functions.Supported by the National Natural Science Foundation of China.

Keywords:	Hyperbolic metric Extremal function Bloch constant
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