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

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


A criterion for the boundedness of singular integrals on hypersurfaces

Author: Stephen W. Semmes
Journal: Trans. Amer. Math. Soc. 311 (1989), 501-513
MSC: Primary 42B20; Secondary 42B25
MathSciNet review: 948198
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: This paper gives geometric conditions on a hypersurface in $ {{\mathbf{R}}^n}$ so that certain singular integrals on that hypersurface define bounded operators on $ {L^2}$. These singular integrals include the Cauchy integral operator in the sense of Clifford analysis and in particular the double layer potential. For curves in the plane, this condition is more general than the chord-arc condition but less general than the Ahlfors-David condition. The main tool is the $ T(b)$ theorem [DJS].

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

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 42B20, 42B25

Retrieve articles in all journals with MSC: 42B20, 42B25

Additional Information

PII: S 0002-9947(1989)0948198-0
Article copyright: © Copyright 1989 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia