β级α型λ-Bazilievic 函数的对数系数

The Logarithmic Coefficients of\ \lambda-Bazilievi\checkc Functions of Type\ \alpha and Order\ \beta

摘要: 利用从属关系给出~\left|\left(g(z)/f(z)\right)^\alpha\right| 的估计,并运用构造一个非负函数和对复变函数模的积分进行估计的方法, 对\ \beta 级\ \alpha 型\ \lambda-Bazilevi\checkc 函数类\ B(\lambda,\alpha,\beta)的对数系数~b_n 进行研究, 得到~|b_n|\leq A\mathrmlogn/n+B/n+32\beta/(1-|1-2\beta|), 其中~A,B 是绝对常数, 推广了相关结果.

Abstract: Estimation of \left|\left(g(z)/f(z)\right)^\alpha\right| is given by using subordination. Using the method of construction a non-negative function and estimation the integration of model of a complex function, the logarithm coefficient b_n of \ \lambda-Bazilevi\checkc Functions of Type\ \alpha and Order\ \beta is studied. The estimate ~|b_n|\leq A\mathrmlogn/n+B/n+32\beta/(1-|1-2\beta|) is given, where A,B are absolute constants.