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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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A criterion for the boundedness of singular integrals on hypersurfaces
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by Stephen W. Semmes PDF
Trans. Amer. Math. Soc. 311 (1989), 501-513 Request permission

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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Additional Information
  • © Copyright 1989 American Mathematical Society
  • 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