J Austral Math Soc Ser A 59 pp112--117, 1995.

Normal Families of Holomorphic Functions

Huai-Hui Chen and Xin-Hou Hua

Abstract

Let a(z) be a meromorphic function with only simple poles, and let k Î N. Suppose that f(x) is meromorphic. We first set up an inequality in which T(r,f) is bounded by the counting function of the zeros of f^(k) + af², and then we prove a corresponding normal criterion. An example shows that the restriction on the poles of a(z) is best possible.

1991 AMS Subject Classification: 30D45, 30D35

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Authors

Huai-Hui Chen

Department of Mathematics, Nanjing Normal University, Nanjing, 210024, P. R. China.

Xin-Hou Hua

Department and Institute of Mathematics, Nanjing University, Nanjing 210008, P. R. China.