一类定义在特殊解析函数族上的积分算子

INTEGRAL OPERATORS DEFINED ON A CLASS OF SPECIAL ANALYTIC FUNCTIONS

设S表示在单位圆D ={z :|z|<1}内单叶解析函数 f(z) =z +∑∞n =2 anzn 的全体组成的族 .引进S的一个新子族Aα(A ,B) ,对该族证明了函数 f(z)∈Aα(A ,B)当且仅当zf′(z) ∈Bα(A ,B) (Bazilevich函数 ) ,并研究了积分算子 .

S denotes the class of functions f(z)=z+∑∞n=2a n?z n which aer univalent analytic functions on D={z:|z|<1} .In this paper,we introduce a new subclass A α(A,B) of S ,prove that the function f(z)∈A α(A,B) if and only if z?f′(z)∈B α(A,B) (Bazilevich function),and conduct a further study for the integral operators on the class of functions.