Cauchy integrals on Lipschitz curves and related operators

A P Calderón

doi:10.1073/pnas.74.4.1324

Cauchy integrals on Lipschitz curves and related operators

Proc Natl Acad Sci U S A. 1977 Apr;74(4):1324-7. doi: 10.1073/pnas.74.4.1324.

Author

A P Calderón¹

Affiliation

¹ Department of Mathematics, University of Chicago, Chicago, Illinois 60637.

Abstract

In this note, we establish certain properties of the Cauchy integral on Lipschitz curves and prove the L(p)-boundedness of some related operators. In particular, we obtain the recent results of R. R. Coifman and Y. Meyer [(1976) "Commutateurs d'intégrales singulières:" Analyse harmonique d'Orsay n(o) 211, Université Paris XI] on the continuity of the so-called commutator operators.