Quasinormal Families of Meromorphic Functions

Xuecheng Pang; Shahar Nevo; Lawrence Zalcman

doi:10.4171/rmi/422

JournalsrmiVol. 21, No. 1pp. 249–262

Quasinormal Families of Meromorphic Functions

Xuecheng Pang
East China Normal University, Shanghai, China
Shahar Nevo
Bar-Ilan University, Ramat-Gan, Israel
Lawrence Zalcman
Bar-Ilan University, Ramat-Gan, Israel

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Abstract

Let $F$ be a family of functions meromorphic on the plane domain $D$ , all of whose zeros are multiple. Suppose that $f^{'} (z) \neq = 1$ for all $f \in F$ and $z \in D .$ Then if $F$ is quasinormal on $D$ , it is quasinormal of order 1 there.

Cite this article

Xuecheng Pang, Shahar Nevo, Lawrence Zalcman, Quasinormal Families of Meromorphic Functions. Rev. Mat. Iberoam. 21 (2005), no. 1, pp. 249–262

DOI 10.4171/RMI/422