We study the relation between the boundary of a simply connected domainΩbeing Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk...We study the relation between the boundary of a simply connected domainΩbeing Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk△onto the domainΩ.As an application,we characterize the chord-arc curves with small norms and the asymptotically smooth curves in terms of the complex dilatation of some quasiconformal reflection with respect to the curve.展开更多
基金National Natural Science Foundation of China (Grant No. 11501259)。
文摘We study the relation between the boundary of a simply connected domainΩbeing Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk△onto the domainΩ.As an application,we characterize the chord-arc curves with small norms and the asymptotically smooth curves in terms of the complex dilatation of some quasiconformal reflection with respect to the curve.
