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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles 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 1.48.

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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


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].
    F. Brackx, R. Delanghe, and F. Sommer, Clifford analysis, Pitman, 1982.
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  • Guy David, Opérateurs intégraux singuliers sur certaines courbes du plan complexe, Ann. Sci. École Norm. Sup. (4) 17 (1984), no. 1, 157–189 (French). MR 744071
  • —, Opérateurs d’intégrale singulière sur les surfaces régulières, Ann. Sci. École Norm. Sup. (to appear).
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  • —, Calerón-Zygmund operators, para-accretive functions, and interpolation, preprint.
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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:
  • MathSciNet review: 948198