On the corona theorem on smooth curves
Complex Variables
2018-11-13 v1
Abstract
We prove the corona theorem for domains whose boundary lies in certain smooth quasicircles. These curves, which are not necessarily Dini-smooth, are defined by quasiconformal mappings whose complex dilatation verifies certain conditions. Most importantly we do not assume any "thickness" condition on the boundary domain. In this sense, our results complement those obtained by Garnett and Jones (1985) and C. Moore on curves (1987).
Cite
@article{arxiv.1811.04434,
title = {On the corona theorem on smooth curves},
author = {J. M. Enriquez-Salamanca and Maria J. Gonzalez},
journal= {arXiv preprint arXiv:1811.04434},
year = {2018}
}
Comments
To appear in Journal of Geometric Analysis 2018