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International Journal of Mathematics and Mathematical Sciences
Volume 2004, Issue 48, Pages 2537-2546
http://dx.doi.org/10.1155/S0161171204401124

Multivalent functions and QK spaces

Department of Mathematics, Shantou University, Shantou, Guangdong 515063, China

Received 13 January 2004

Copyright © 2004 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

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.