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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
Affiliation:
Department of Mathematics Education, Yeungnam University, 214-1 Daedong, Gyongsan 712-749, Korea ([email protected])
Toshiyuki Sugawa
Affiliation:
Department of Mathematics, Graduate School of Science, Hiroshima University, Higashi-Hiroshima 739-8526, Japan ([email protected])
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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.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 2006