Ahlfors-regular curves and Carleson measures
Complex Variables
2018-07-09 v2
Abstract
We study the relation between the boundary of a simply connected domain being Ahlfors-regular and the invariance of Carleson measures under the push-forward operator induced by a conformal mapping from the unit disk onto the domain. As an application, we characterize the chord-arc curve with small norm and the asymptotically smooth curve in terms of the complex dilatation of some quasiconformal reflection with respect to the curve.
Keywords
Cite
@article{arxiv.1804.06671,
title = {Ahlfors-regular curves and Carleson measures},
author = {Huaying Wei and Michel Zinsmeister},
journal= {arXiv preprint arXiv:1804.06671},
year = {2018}
}
Comments
11 pages