解析函数中的Bohr型不等式的生成  

Generalization of Bohr-type Inequality in Analytic Functions

作　　者：林柔苑 刘名生[1] Saminathan PONNUSAMY Rou Yuan LIN;Ming Sheng LIU;Saminathan PONNUSAMY(School of Mathematical Sciences,South China Normal University,Guangzhou 510631,P.R.China;Department of Mathematics,Indian Institute of Technology Madras,Chennai600036,India;Lomonosou Moscow State University,Moscow Center of Fundamental and Applied Mathematics,Moscow,Russia)

机构地区：[1]华南师范大学数学科学学院,广州510631 [2]印度理工学院马德拉斯分校数学系,清奈600036 [3]罗蒙诺索夫莫斯科国立大学莫斯科基础和应用数学中心,莫斯科

出　　处：《数学学报（中文版）》2023年第3期455-474,共20页Acta Mathematica Sinica：Chinese Series

基　　金：广东省自然科学基金资助项目(2021A1515010058)。

摘　　要：利用非负连续函数{ζ_(n)(r)}n≥0加细在单位圆盘|z|<1内满足Ref(z)<1的解析函数类的玻尔半径,和加细在单位圆盘|z|<1内形如∑^(n=0)^(∞)a_(pn+m)z^(pn+m)的解析函数的交错级数A_(f)(r)的玻尔半径.在后一种情况,本文也得到了偶和奇解析函数的玻尔半径的信息.进一步,建立了优级数Mf(r)与f(z)的奇数位和偶数位的关系,并将证明本文的大部分结果都是精确的.We mainly use the nonnegative continuous function{ζ_(n)(r)}n≥0to redefine the Bohr radius for the class of analytic functions satisfying Ref(z)<1 in the unit disk Izl<1 and redefine the Bohr radius of the alternating series A_(f)(r)with analytic functions f of the form f(z)=∑^(n=0)^(∞)a_(pn+m)z^(pn+m)in/|z|<1.In the latter case,one can also get information about Bohr radius for even and odd analytic functions.Moreover,the relationships between the majorant series M_(f)(r)and the odd and the even bits of f(z)are also established.We will prove that most of results are sharp.

关 键 词：玻尔半径 有界解析函数 交错级数 玻尔不等式 

分 类 号：O174.51[理学—数学]