A Note on a Theorem of Chuaqui and Gevirtz

Abstract

For a subdomain Ω 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) ⊂ Ω if and only if there exists a compact subset K of H such that sK ∩ (H \ Ω) 6= ∅ for any positive number s. We show that this condition is equivalent to the inequality W (Ω) < 2, where W (Ω) stands for the circular width of the domain Ω.

Cite this paper

@inproceedings{Kim2008ANO, title={A Note on a Theorem of Chuaqui and Gevirtz}, author={Yong Chan Kim and Toshiyuki Sugawa}, year={2008} }