一个线性算子及其相关的亚纯多叶函数类

A linear operator and its families of meromorphically multivalent functions

引进单位圆盘内亚纯p叶函数的子类Tn,p(A,B),分别研究其包含关系及类中函数的积分变换性质,得到两个结论:若n≥p(A-2B-1)1+B,则Tn+1,p Tn,p(A,B);若f∈Tn,p(A,B),则函数g(z)被定义成∫z也在类Tn,p(A,B)中.tλ-1[Dn+p-1f(t)]βdt1/βDn+p-1g(z)

In this paper a subclass T_(n,p)(A,B) of meromorphically p-valent functions in the unit disc is introduced and certain properties of this class such as inclusion relations and integral transforms are studied. Two results are obtained: if n≥p(A-2B-1)1+B, then T_(n+1,p)(A,B)T_(n,p)(A,B); and if (f∈)T_(n,p)(A,B), then the function g(z) defined by D^(n+p-1)g(z)=λ-pβz~λ∫~z_0t^(λ-1)[D^(n+p-1)f(t)]~βdt^(1/β) is in the same class T_(n,p)(A,B).