Annales Academić Scientiarum Fennicć
Mathematica
Volumen 33, 2008, 273-279

A NOTE ON A THEOREM OF CHUAQUI AND GEVIRTZ

Yong Chan Kim and Toshiyuki Sugawa

Yeungnam University, Department of Mathematics Education
214-1 Daedong Gyongsan 712-749, Korea; kimyc 'at' yumail.ac.kr

Hiroshima University, Graduate School of Science, Department of Mathematics
Higashi-Hiroshima, 739-8526 Japan; sugawa 'at' math.sci.hiroshima-u.ac.jp

Abstract. For a subdomain \Omega of the right half-plane H, Chuaqui and Gevirtz showed the following theorem: the image f(D)$ of the unit disk D under an analytic function f on D is a quasidisk whenever f'(D)\subset\Omega if and only if there exists a compact subset K of H such that sK\cap(H \ \Omega)\not\equal\emptyset for any positive number s. We show that this condition is equivalent to the inequality W(\Omega) < 2, where W(\Omega) stands for the circular width of the domain \Omega.

2000 Mathematics Subject Classification: Primary 30F45; Secondary 30C35.

Key words: Noshiro-Warschawski theorem, quasidisk, pre-Schwarzian derivative.

Reference to this article: Y.C. Kim and T. Sugawa: A note on a theorem of Chuaqui and Gevirtz. Ann. Acad. Sci. Fenn. Math. 33 (2008), 273-279.

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