一类解析函数的Bohr定理

定义单位开圆盘D内的一个解析函数类P_α(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P_α(D)上的Bohr半径r₀.特别地,当α=1/2时,r₀=1/3,推广了凸函数的Bohr半径.

Bohr Theorem for A Class of Analytic Functions

The class P_α(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 r₀. In particular, r₀=1/3 when α=1/2, which extends the Bohr radius of convex functions.