Hostname: page-component-7bb8b95d7b-wpx69 Total loading time: 0 Render date: 2024-09-27T06:06:05.102Z Has data issue: false hasContentIssue false
  • English
  • Français

Meromorphic Lipschitz functions

Published online by Cambridge University Press:  17 April 2009

Shinji Yamashita
Shinji Yamashita
Affiliation:
Department of Mathematics, Tokyo Metropolitan University, Fukasawa, Setagaya, Tokyo 158, Japan
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let f be a function meromorphic in D = {|z| < 1} and let X be the chordal distance on the Riemann sphere. Then f satisfies the Lipschitz condition

in D if and only if |f′(z)|/(1 + |f(z)|2) = O((1 – |z|)α−1) and |z| → 1.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 38 , Issue 3 , December 1988 , pp. 451 - 455
Copyright
Copyright © Australian Mathematical Society 1988

References

[1]Goluzin, G.M., Geometric theory of functions of a complez variable (Trans. Math. Monographs 26, Amer. Math. Soc., Providence, 1969).CrossRefGoogle Scholar
[2]Yamashita, S., ‘Smoothness of the boundary values of functions bounded and holomorphic in the disk’, Trans. Amer. Math. Soc. 272 (1982), 539–544.CrossRefGoogle Scholar