In this paper we establish estimates for normal K-quasiconformal mappings of any finitely-connected domain in the extended -plane onto the interior or exterior of the unit circle or the extended -plane with slits on the circles . The bounds in the estimates for , etc. are explicitly given. They are sharp or asymptotically sharp and deduced mainly from estimates for the inverse mappings of in our previous paper  based on Carleman’s and Gr¨otzsch’s inequalities and partly improved here. A generalization of the Schwarz lemma and improvements of some classical inequalities for conformal mappings are shown.
Cite this article
Vo Dang Thao, Estimates for Quasiconformal Mappings onto Canonical Domains (II). Z. Anal. Anwend. 21 (2002), no. 4, pp. 1043–1054DOI 10.4171/ZAA/1125