Extra cancellation of even Calderón-Zygmund operators and Quasiconformal mappings
نویسندگان
چکیده
In this paper we discuss a special class of Beltrami coefficients whose associated quasiconformal mapping is bilipschitz. A particular example are those of the form f(z)χΩ(z), where Ω is a bounded domain with boundary of class C1+ε and f a function in Lip(ε,Ω) satisfying ‖f‖∞ < 1. An important point is that there is no restriction whatsoever on the Lip(ε,Ω) norm of f besides the requirement on Beltrami coefficients that the supremum norm be less than 1. The crucial fact in the proof is the extra cancellation enjoyed by even homogeneous Calderón-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. An application to a Lipschitz regularity result for solutions of second order elliptic equations in divergence form in the plane is presented.
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