Yan Xu
Abstract. In this paper, we prove the following theorem: Let F
be a family of holomorphic functions in the unit disc D and let a be a nonzero complex number. If, for any
f ÎF,
f(z)= a
Þ
f'(z)= a, f'(z)= a
Þ
f''(z)= a,
then F is uniformly normal in D , that is, there exists a positive constant M such that
(1-|z|2) f#(z)£M
for each f ÎF and z ÎD where M is independently of M. This result improves related results due to [2], [8], and [3].
2000 Mathematics Subject Classification: 30D45
Full text: PDF
|
