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].References
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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