一类解析函数的Bohr定理

Bohr Theorem for A Class of Analytic Functions

定义单位开圆盘D内的一个解析函数类Pα(D)=f∈A(D):Re f(z)/z≥α(0<α≤1),给出其增长和掩盖定理.作为应用,得到Pα(D)上的Bohr半径r 0.特别地,当α=1/2时,r 0=1/3,推广了凸函数的Bohr半径.

The class Pα(D)=f∈A(D):Re f(z)/z≥α(0<α≤1)of analytic functions in the open unit disk D is introduced.We establish the growth and covering theorem for this analytic function class.As an application,we obtain the Bohr radius r 0.In particular,r 0=1/3 whenα=1/2,which extends the Bohr radius of convex functions.