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) 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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