Hardy inequalities for simply connected planar domains
Functional Analysis
2007-05-23 v1 Complex Variables
Abstract
In 1986 A. Ancona showed, using the Koebe one-quarter Theorem, that for a simply-connected planar domain the constant in the Hardy inequality with the distance to the boundary is greater than or equal to 1/16. In this paper we consider classes of domains for which there is a stronger version of the Koebe Theorem. This implies better estimates for the constant appearing in the Hardy inequality.
Keywords
Cite
@article{arxiv.math/0603362,
title = {Hardy inequalities for simply connected planar domains},
author = {Ari Laptev and Alexander V. Sobolev},
journal= {arXiv preprint arXiv:math/0603362},
year = {2007}
}
Comments
9 pages