两类p叶亚纯函数的性质

PROPERTIES FOR TWO CLASSES OF p-VALENTLY MEROMORPHIC FUNCTIONS

首先定义了微分算子Ikp,然后利用这个算子Ikp引入了2类p叶亚纯函数族∑(S)p*-1(k,α,β)及∑(C)p-1(k,α,β),得到这2个函数族的系数不等式,并定义了函数族∑Ghψ(Cn+p).利用函数族∑(S)*p-1(k,α,β)和∑(C)p-1(k,α,β)的系数特征得到结论:有限个∑(S)p*-1(k,α,β)中函数与有限个∑(C)p-1(k,α,β)中函数的卷积包含在函数族∑Ghψ(Cn+p)内,进一步得到其偏差定理和涉及这2类函数的积分变换结论.

The definition of differential operator Ikp is first given,and then two classes of p-valently meromorphic functions ∑（S）＊p-1（k,α,β） and ∑（C）p-1（k,α,β） by means of the operator Ikp are introduced.The coefficient inequalities of this two classes of functions are obtained by applying the analytical method and technique,and the function class ∑Ghψ（Cn＋p） is also introduced.Next by making use of coefficient characterizations of function classes ∑（S）＊p-1（k,α,β） and ∑（C）p-1（k,α,β）,the main conclusions of this paper are derived.That is,the Hadamard product of functions which combined with finite functions in ∑（S）＊p-1（k,α,β） and finite functions in ∑（C）p-1（k,α,β） belongs to the class ∑Ghψ（Cn＋p）.Furthermore,the distortion theorems and integral transforms related to this two classes are provided.