International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 48, Pages 2537-2546
Multivalent functions and spaces
Department of Mathematics, Shantou University, Shantou 515063, Guangdong, China
Received 13 January 2004
Copyright © 2004 Hasi Wulan. 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.
We give a criterion for -valent analytic functions in the unit disk to belong to , a Möbius-invariant space of functions analytic in the unit disk in the plane for a nondecreasing function , and we show by an example that our condition is sharp. As corollaries, classical results on univalent functions, the Bloch space, BMOA, and spaces are obtained.