论文标题
BOHR的不平等现象，用于简单连接的域上的单型界函数
Bohr inequalities for unimodular bounded functions on simply connected domains
论文作者
论文摘要
令$ \ Mathcal {h}（\ Mathbb {d}）$为单位磁盘$ \ Mathbb {d}中的分析函数类：= \ {z \ in \ Mathbb {c}：| z | | <1 \ \} $。经典的bohr的不平等指出，如果功率系列$ f（z）= \ sum_ {n = 0}^{\ infty} a_nz^n $收敛于$ \ mathbb {d} $ and $ | f（z）| <1 $ \ begin {equation*} \ sum_ {n = 0}^{\ infty} | a_n | r^n \ leq 1 \; \; \ mbox {for} \; \; \; r \ leq \ frac {1} {3} \ end {equation*} 而且，常数$ 1/3 $无法改善。常数$ 1/3 $称为Bohr Radius。在本文中，我们研究了简单连接域的分析和谐波映射的BOHR现象。我们证明了改善BOHR半径的分析功能以及简单连接域上的谐波映射的结果。
Let $ \mathcal{H}(\mathbb{D}) $ be the class of analytic functions in the unit disk $ \mathbb{D} : =\{z\in\mathbb{C} : |z|<1\} $. The classical Bohr's inequality states that if a power series $ f(z)=\sum_{n=0}^{\infty}a_nz^n $ converges in $ \mathbb{D} $ and $ |f(z)|<1 $ for $ z\in\mathbb{D} $, then \begin{equation*} \sum_{n=0}^{\infty}|a_n|r^n\leq 1\;\;\mbox{for}\;\; r\leq \frac{1}{3} \end{equation*} and the constant $ 1/3 $ cannot be improved. The constant $ 1/3 $ is known as Bohr radius. In this paper, we study Bohr phenomenon for analytic as well as harmonic mappings on simply connected domains. We prove several sharp results on improved Bohr radius for analytic functions as well as for harmonic mappings on simply connected domains.
