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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
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Abstract

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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