International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 503-510
doi:10.1155/S0161171297000689
Some properties and characterizations of A-normal functions
Department of Mathematics, Peking University, Beijing 100871, China
Received 11 January 1994; Revised 23 October 1995
Copyright © 1997 Jie Xiao. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
Let M be the set of all functions meromorphic on D={z∈ℂ:|z|<1}.
For a∈(0,1], a function f∈M is called a-normal function of bounded (vanishing) type or
f∈Na(N0a), if supz∈D(1−|z|)af#(z)<∞ (lim|z|→1(1−|z|)af#(z)=0). In this paper
we not only show the discontinuity of Na and N0a relative to containment as a varies, which
shows ∪0<a<1Na⊂UBC0, but also give several characterizations of Na and N0a which are real
extensions for characterizations of N and N0.