Distortion theorems for locally univalent Bloch functions |
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| Authors: | Mario Bonk David Minda Hiroshi Yanagihara |
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| Institution: | (1) Institut für Analysis, Tech. Univ. Braunschweig, 38106 Braunschweig, Germany;(2) Department of Mathematical Sciences, University of Cincinnati, 45221-0025 Cincinnati, OH, USA;(3) Department of Applied Science Faculty of Engineering, Yamaguchi University, Tokiwadai, Ube, Japan |
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| Abstract: | A holomorphic functionf defined on the unit disk d is called a Bloch function provided {fx73-02} For α ∃ (0,1] letB∞(α)denote the class of locally univalent Bloch functionsf normalized by ∥f∥B ≤1f(0) = 0 andf’(0) = α. A type of subordination theorem is established for B∞(α). This subordination theorem is used to derive sharp growth,
distortion, curvature and covering theorems for B∞(α).
Supported as a Feodor Lynen Fellow of the Alexander von Humboldt Foundation.
Research supported in part by a National Science Foundation grant. |
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