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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 3, Pages 503-510
http://dx.doi.org/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 Hindawi Publishing Corporation. 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:|z|<1}. For a(0,1], a function fM is called a-normal function of bounded (vanishing) type or fNa(N0a), if supzD(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<1NaUBC0, but also give several characterizations of Na and N0a which are real extensions for characterizations of N and N0.