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The Cauchy Integral, Calderon Commutators, and Conjugations of Singular Integrals in R n
Journal article   Peer reviewed

The Cauchy Integral, Calderon Commutators, and Conjugations of Singular Integrals in R n

Margaret A. M. Murray
Transactions of the American Mathematical Society, Vol.289(2), p.497
06/1985
DOI: 10.2307/2000250

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Abstract

We consider the Cauchy integral and Hilbert transform for Lipschitz domains in the Clifford algebra based on Rn. The Hilbert transform is shown to be the generating function for the Calderón commutators in Rn. We make use of an intrinsic characterization of these commutators to obtain L2 estimates. These estimates are used to show the analyticity of the Hilbert transform and of th conjugation of singular integral operators by bi-Lipschitz changes of variable in Rn.

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