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) ≠ φ 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.
|Number of pages||7|
|Journal||Annales Academiae Scientiarum Fennicae Mathematica|
|Publication status||Published - 2008 Dec 1|
- Noshiro-Warschawski theorem
- Pre-Schwarzian derivative
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