两类解析函数的卷积性质

Convolution Properties of Two Classes of Analytic Functions

设a<1,以R(a)表示单位圆盘D={|z|<1}内解析且满足f(0)=f′(0)-1=0,Ref′(z)>a,z∈D的函数f(z)的全体.以U(a)表示D内解析且满足f(0)=f′(0)-1=0,Re[f′(z)+zf″(z)]>a,z∈D的函数f(z)的全体.本文研究了R(a)与U(a)类函数的卷积性质。

Let R(α), α<l, denote the class of functions f(z) which are analytic in the unit disk D = {|z|<1} and satisfy f(0)=f'(0)-1=0, Ref'(z)>α, zeD. Let U(α), α <1, denote the class of functions f(z) which are analytic in D and satisfy f(0) =f'(0) -1=0, Re[f'(z) +zf'(z)]>α, zeD. Some convolution properties of these two classes of functions are given in this paper.