Some estimates for normalized quasiconformal self-mappings of the unit disk

Abstract

In this article, we provide an integral estimate for the boundary values of a normalized quasiconformal self-mapping of the unit disk. Estimates are also given for the partial derivative of the Douady–Earle extension.

Keywords:

• Douady–Earle extension
• quasiconformal mapping

2000 Mathematics subject classifications::

• 30A10
• 30C62
• 30E20

Acknowledgements

This article forms part of the author's PhD thesis. He is indebted to his supervisor Professor Aimo Hinkkanen for the invaluable guidance and many enlightening discussions. This research has been partially supported by the grant 07305 from the Campus Research Board of the University of Illinois at Urbana–Champaign.