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Square function estimates and the  theorem
Author:
Stephen Semmes
Journal:
Proc. Amer. Math. Soc. 110 (1990), 721-726
MSC:
Primary 42B20; Secondary 46E99, 47G10
MathSciNet review:
1028049
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Abstract: A very simple proof is given of the sort of square function estimates provided by the  theorem. The approach is based on the bilinear methods of Coifman and Meyer. Among the applications is an easy proof of the boundedness of the Cauchy integral operator on Lipschitz graphs.
- [CM]
R. Coifman and Y. Meyer, Au-delà des opérateurs pseudo-différentials, Astérisque 57 (1978).
- [CMM]
R.
R. Coifman, A.
McIntosh, and Y.
Meyer, L’intégrale de Cauchy définit un
opérateur borné sur 𝐿² pour les courbes
lipschitziennes, Ann. of Math. (2) 116 (1982),
no. 2, 361–387 (French). MR 672839
(84m:42027), http://dx.doi.org/10.2307/2007065
- [DJS]
G.
David, J.-L.
Journé, and S.
Semmes, Opérateurs de Calderón-Zygmund, fonctions
para-accrétives et interpolation, Rev. Mat. Iberoamericana
1 (1985), no. 4, 1–56 (French). MR 850408
(88f:47024), http://dx.doi.org/10.4171/RMI/17
- [MM]
Alan
McIntosh and Yves
Meyer, Algèbres d’opérateurs définis par
des intégrales singulières, C. R. Acad. Sci. Paris
Sér. I Math. 301 (1985), no. 8, 395–397
(French, with English summary). MR 808636
(87b:47053)
- [J]
Peter
W. Jones, Square functions, Cauchy integrals, analytic capacity,
and harmonic measure, Harmonic analysis and partial differential
equations (El Escorial, 1987), Lecture Notes in Math., vol. 1384,
Springer, Berlin, 1989, pp. 24–68. MR 1013815
(91b:42032), http://dx.doi.org/10.1007/BFb0086793
- [S]
Stephen
W. Semmes, A criterion for the boundedness of
singular integrals on hypersurfaces, Trans.
Amer. Math. Soc. 311 (1989), no. 2, 501–513. MR 948198
(89k:42017), http://dx.doi.org/10.1090/S0002-9947-1989-0948198-0
- [CM]
- R. Coifman and Y. Meyer, Au-delà des opérateurs pseudo-différentials, Astérisque 57 (1978).
- [CMM]
- R. Coifman, A. McIntosh, and Y. Meyer, L'integrale de Cauchy définit un opérateur borné sur
 pour les courbes Lipschitziennes, Ann. Math. 116 (1982), 361-388. MR 672839 (84m:42027)
- [DJS]
- G. David, J. L. Journé, and S. Semmes, Operateurs de Calderón-Zygmund, fontions para-accretives et interpolation, Revista Mat. Iberoamericana 1 (1985), 1-56. MR 850408 (88f:47024)
- [MM]
- A. McIntosh and Y. Meyer, Algèbres d'opérateurs définis par des intégrales singuliéres, Comptes Rendus Acad. Sci. Paris 301 (1985), 395-397. MR 808636 (87b:47053)
- [J]
- P. Jones, Square functions, Cauchy integrals, analytic capacity, and harmonic measure, in Harmonic Analysis and Partial Differential Equations (J. Garciá-Cuerra, ed.). Lecture Notes in Math., vol. 1384, Springer-Verlag, 1989. MR 1013815 (91b:42032)
- [S]
- S. Semmes, A criterion for the boundedness of singular integrals on hypersurfaces, Trans. Amer. Math. Soc. 311 (1989), 501-513. MR 948198 (89k:42017)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0002-9939-1990-1028049-2
PII:
S 0002-9939(1990)1028049-2
Article copyright:
© Copyright 1990 American Mathematical Society
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