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Unbounded analytic functions on plane domains

Part of: Geometric function theory

Published online by Cambridge University Press:  26 February 2010

J. D. Hinchliffe
J. D. Hinchliffe
Affiliation:
School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK
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Abstract

A function is called strongly unbounded on a domain D if there exists a sequence in D on which f and all its derivatives tend to infinity. A result of Gordon is generalized to show that an unbounded analytic function on a quasidisk is always strongly unbounded there.

MSC classification

Secondary: 30C62: Quasiconformal mappings in the plane
Type
Research Article
Information
Mathematika , Volume 50 , Issue 1-2 , December 2003 , pp. 207 - 214
Copyright
Copyright © University College London 2003

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References

1.Ahlfors, L. V.. Lectures on Quasiconformal Mappings. Wadsworth & Brooks/Cole Advanced Books & Software (Monterey, CA, 1987).Google Scholar
2.Duren, P. L.. Theory of Hp Spaces. Academic Press (New York, 1970).Google Scholar
3.Fait, M., Krzyz, J. G. and Zygmunt, J.. Explicit quasiconformal extensions for some classes of univalent functions. Comment. Math, llelv., 51 (1976) 279285.CrossRefGoogle Scholar
4.Gordon, A. Ya.. Strong unboundedness of unbounded analytic functions. Proc. Ainer. Math. Soc, 122 (1994) 525–529.Google Scholar
5.Langley, J. K.. Composite Bank-Laine functions and a question of Rubcl. Trans. Amer. Math. Soc, 354(2002) 1177–1191.CrossRefGoogle Scholar
6.Pommerenke, Ch.. Boundary Behaviour of Conformal Maps. Springer–Verlag (Berlin. 1992).Google Scholar
7.Rubel, L. A.. Unbounded analytic functions and their derivatives on plane domains. Bull. Insi. Math. Acad. Sinica, 12 (1984) 363377.Google Scholar