Bohr radius for locally univalent harmonic mappings

被引：66

作者：

Kayumov, Ilgiz R. ^{[1
]}

Ponnusamy, Saminathan ^{[2
]}

Shakirov, Nail ^{[1
]}

机构：

[1] Kazan Fed Univ, Kremlevskaya 18, Kazan 420008, Russia

[2] Indian Inst Technol Madras, Dept Math, Madras 600036, Tamil Nadu, India

来源：

MATHEMATISCHE NACHRICHTEN | 2018年 / 291卷 / 11-12期

基金：

俄罗斯基础研究基金会;

关键词：

Bloch space; Bohr radius; harmonic; locally univalent; and analytic functions; K-quasiconformal mappings; Schwarz lemma; BLOCH FUNCTIONS; POWER-SERIES; CONSTANT; THEOREM;

D O I：

10.1002/mana.201700068

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We consider the class of all sense-preserving harmonic mappings f=h+g of the unit disk D, where h and g are analytic with g(0)=0, and determine the Bohr radius if any one of the following conditions holds: h is bounded in D.h satisfies the condition Re h(z)1 in D with h(0)>0.both h and g are bounded in D.h is bounded and g(0)=0. 1.2.3.4.We also consider the problem of determining the Bohr radius when the supremum of the modulus of the dilatation of f in D is strictly less than 1. In addition, we determine the Bohr radius for the space B of analytic Bloch functions and the space BH of harmonic Bloch functions. The paper concludes with two conjectures.

引用

页码：1757 / 1768

页数：12

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