Cauchy-Stieltjes积分和面积平均p叶函数

董新汉;杨密

数学学报 ›› 2005, Vol. 48 ›› Issue (5) : 851-858.

PDF(391 KB)
PDF(391 KB)
数学学报 ›› 2005, Vol. 48 ›› Issue (5) : 851-858. DOI: 10.12386/A2005sxxb0103
论文

Cauchy-Stieltjes积分和面积平均p叶函数

    董新汉;杨密
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Cauchy-Stieltjes Integrals and Areally Mean p-Valent Functions

    Xin Han DONG, Mi YANG
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摘要

本文研究由Cauchy-Stieltjes积分形成的函数空间Fα.首先给出这个空间的一个等价定义,然后研究面积平均p叶函数的对数函数和这个函数空间的关系,最后对单叶函数的情形做进一步的讨论.根据这种研究,我们得到了有界单叶函数的系数增长估计,这是目前最好的结果.

Abstract

We consider the function space Fα consisting of Cauchy-Stieltjes integrals. First, we give an equivalent definition of this space, then study the relation between this space and the logarithmic function of areally mean p-valent function, and finally we discuss further this relation for the case of univalent functions. From this investigation, we obtain a growth estimation about the coefficients of bounded univalent functions, which is the best result up to now.

关键词

面积平均p叶函数 / Cauchy-Stieltjes积分 / 单叶函数

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董新汉;杨密. Cauchy-Stieltjes积分和面积平均p叶函数. 数学学报, 2005, 48(5): 851-858 https://doi.org/10.12386/A2005sxxb0103
Xin Han DONG, Mi YANG. Cauchy-Stieltjes Integrals and Areally Mean p-Valent Functions. Acta Mathematica Sinica, Chinese Series, 2005, 48(5): 851-858 https://doi.org/10.12386/A2005sxxb0103
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