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Criteria for functions to be Bloch

Published online by Cambridge University Press:  17 April 2009

Shinji Yamashita
Shinji Yamashita
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Fukazawa, Setagaya, Tokyo 158, Japan.
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Abstract

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Criteria for a holomorphic function f defined in |z| < 1 to be Bloch, namely, , are obtained in terms of the area and the length of the images of non-Euclidean disks and non-Euclidean circles, respectively.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 21 , Issue 2 , May 1980 , pp. 223 - 227
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Anderson, J.M., Clunie, J. and Pommerenke, Ch., “On Bloch functions and normal functions”, J. Reine Angew. Math. 270 (1974), 12–37.Google Scholar
[2]Lappan, Peter, “A non-normal locally uniformly univalent function”, Bull. London Math. Soc. 5 (1973), 291–294.CrossRefGoogle Scholar
[3]MacGregor, Thomas H., “Length and area estimates for analytic functions”, Michigan Math. J. 11 (1964), 317–320.CrossRefGoogle Scholar
[4]Pommerenke, Ch., “On Bloch functions”, J. London Math. Soc. (2) 2 (1970), 689–695.CrossRefGoogle Scholar
[5]Timoney, Richard M., “A necessary and sufficient condition for Bloch functions”, Proc. Amer. Math. Soc. 71 (1978), 263–266.CrossRefGoogle Scholar