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arXiv · 0802.1185

Extra cancellation of even Calderon-Zygmund operators and quasiconformal mappings

Joan Mateu·Joan Orobitg·Joan Verdera
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Abstract

We discuss a special class of Beltrami coefficients whose associated quasiconformal mapping is bilipschitz. These are of the form the characteristic function of a planar bounded domain with smooth boundary of class C 1+epsilon times a density of class Lip epsilon on the domain. The crucial fact in the argument is the special extracancellation property of even Calderon-Zygmund kernels, namely that they have zero integral on half the unit ball. This property is expressed in a particularly suggestive way and is shown to have far-reaching consequences. The main result may also be viewed as a Lipschitz regularity result for the Beltrami equation, and so for certain planar second order elliptic equations in divergence form.

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Joan Mateu, Joan Orobitg, Joan Verdera. 2008-10-01. Extra cancellation of even Calderon-Zygmund operators and quasiconformal mappings. https://arxiv.org/abs/0802.1185

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