Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42B20, 47B38, 47G05

Retrieve articles in all journals with MSC: 42B20, 47B38, 47G05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0784001-6
PII: S 0002-9947(1985)0784001-6
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