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Transactions of the American Mathematical Society

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The Cauchy integral, Calderón commutators, and conjugations of singular integrals in $ {\bf R}\sp n$

Author: Margaret A. M. Murray
Journal: Trans. Amer. Math. Soc. 289 (1985), 497-518
MSC: Primary 42B20; Secondary 47B38, 47G05
MathSciNet review: 784001
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Abstract: We consider the Cauchy integral and Hilbert transform for Lipschitz domains in the Clifford algebra based on $ {R^n}$. The Hilbert transform is shown to be the generating function for the Calderón commutators in $ {R^n}$. We make use of an intrinsic characterization of these commutators to obtain $ {L^2}$ estimates. These estimates are used to show the analyticity of the Hilbert transform and of the conjugation of singular integral operators by bi-Lipschitz changes of variable in $ {R^n}$.

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Keywords: Commutators with singular integrals in $ {R^n}$, Cauchy integrals in $ {R^n}$, conjugation of singular integrals by changes of variable
Article copyright: © Copyright 1985 American Mathematical Society