中文摘要：

主要证明了以下的定理：设F为复平面上一区域上F的亚纯函数族,k为正整数,a为非零有穷复数,F中的每一个f的零点和极点的重级均k＋2,记L（f）=a0f（k）＋a1f（k-1）＋…＋akf,其中a0≠0,a1,…,ak为复数.若对任意的f,g∈F,L（f）,L（g）,在D内分担a,则F在D上正规.

英文摘要：

Let F be a family of meromorphic functions defined on a domain D in the complexplane,k be a positive integer and a be a non-zero finite complex number such that each f∈F has zeros and poles of multiplicity at least k＋2.Denote L（f）=a0（f）（k）＋…＋akf,where a0≠0,a1,…,ak are finite complex numbers.Suppose that L（f） and L（g） share ＂a＂ on D for any f and g in F,then F is a normal family on D.