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Cauchy-Stieltjes积分和面积平均p叶函数 被引量：1

Cauchy-Stieltjes Integrals and Areally Mean p-Valent Functions
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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. 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.
作者 董新汉 杨密
机构地区 湖南师范大学数学与计算机科学学院
出处 《数学学报（中文版）》 SCIE CSCD 北大核心 2005年第5期851-858,共8页 Acta Mathematica Sinica：Chinese Series
基金 国家自然科学基金资助项目(19871026)
关键词 CAUCHY-STIELTJES积分 面积平均P叶函数 单叶函数 Cauchy Stieltjes integral Areally mean p-valent function Univalent function
分类号 O174.56 [理学—基础数学]
  • 相关文献

参考文献25

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同被引文献8

  • 1[1]D J Hallenbeck,T H Macgregor.Linear problems and convexity techniques in geometric function Theory[M].New York:Putnam Publishing,1984.
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  • 3[3]R A Hibschweiler,T H Macgregor.Multipliers of families of Cauchy-stieltjes transforms[J].Tran Amer Math Soc,1992,(331):377-394.
  • 4[4]D J Hallenbeck,T H Macgregor,K Samotij.Fractional cauchy transforms inner functions and multipliers[J].Proc London Math Soc,1996,72(3):157-187.
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  • 7[7]D J Hallenbeck,K Samotij.On Cauchy integrals of logarithmic potentials and their multipliers[J].J Math Anal Appl,1993,(174):614-634.
  • 8[9]X H Dong,K S Lau.Cauchy transforms of self-similar measures:the Laurent coefficients[J].J Funct Anal,2003,(202):67-97.

引证文献1

数学学报（中文版）
2005年 第5期

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