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NORM ESTIMATES OF THE PRE-SCHWARZIAN DERIVATIVES FOR CERTAIN CLASSES OF UNIVALENT FUNCTIONS

Published online by Cambridge University Press:  02 February 2006

Yong Chan Kim  and
Toshiyuki Sugawa
Yong Chan Kim
Affiliation:
Department of Mathematics Education, Yeungnam University, 214-1 Daedong, Gyongsan 712-749, Korea (kimyc@yu.ac.kr)
Toshiyuki Sugawa
Affiliation:
Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan (sugawa@math.sci.hiroshima-u.ac.jp)
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Abstract

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A sharp norm estimate will be given to the pre-Schwarzian derivatives of close-to-convex functions of specified type. In order to show the sharpness, we introduce a kind of maximal operator which may be of independent interest. We also discuss a relation between the subclasses of close-to-convex functions and the Hardy spaces.

Keywords

Primary 30C45Secondary 30A32pre-Schwarzian derivativeuniformly locally univalentclose-to-convex function
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 49 , Issue 1 , February 2006 , pp. 131 - 143
Copyright
Copyright © Edinburgh Mathematical Society 2006