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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
DOI: https://doi.org/10.1090/S0002-9947-1989-0948198-0
MathSciNet review: 948198
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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].


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DOI: https://doi.org/10.1090/S0002-9947-1989-0948198-0
Article copyright: © Copyright 1989 American Mathematical Society