Hostname: page-component-78c5997874-8bhkd Total loading time: 0 Render date: 2024-11-05T01:48:08.212Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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