International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 48, Pages 2537-2546
doi:10.1155/S0161171204401124
Multivalent functions and QK 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.
Abstract
We give a criterion for q-valent analytic functions in the unit disk to belong to QK, a Möbius-invariant space of functions analytic in the unit disk in the plane for a nondecreasing function K:[0,∞)→[0,∞), and we show by an example that our condition is sharp. As corollaries, classical results on univalent functions, the Bloch space, BMOA, and Qp spaces are obtained.