Uniformly locally univalent functions and Hardy spaces

We consider the class of uniformly locally univalent functions on the unit disk with prescribed pre-Schwarzian norm. In the present paper, we show that the class is contained in the Hardy space of a specific exponent depending on the norm.

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2009-05, Vol.353 (1), p.61-67
Main Authors: Kim, Yong Chan, Sugawa, Toshiyuki
Format: Article
Language:English
Subjects:
Exact sciences and technology
Gap series
Hardy space
Mathematical analysis
Mathematics
Pre-Schwarzian derivative
Sciences and techniques of general use
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Description
Summary:We consider the class of uniformly locally univalent functions on the unit disk with prescribed pre-Schwarzian norm. In the present paper, we show that the class is contained in the Hardy space of a specific exponent depending on the norm.
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2008.11.036