Square function estimates and the $T(b)$ theorem
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- by Stephen Semmes PDF
- Proc. Amer. Math. Soc. 110 (1990), 721-726 Request permission
Abstract:
A very simple proof is given of the sort of square function estimates provided by the $T(b)$ 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.References
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R. Coifman and Y. Meyer, Au-delà des opérateurs pseudo-différentials, Astérisque 57 (1978).
- R. R. Coifman, A. McIntosh, and Y. Meyer, LâintĂ©grale de Cauchy dĂ©finit un opĂ©rateur bornĂ© sur $L^{2}$ pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), no. 2, 361â387 (French). MR 672839, DOI 10.2307/2007065
- G. David, J.-L. JournĂ©, and S. Semmes, OpĂ©rateurs de CalderĂłn-Zygmund, fonctions para-accrĂ©tives et interpolation, Rev. Mat. Iberoamericana 1 (1985), no. 4, 1â56 (French). MR 850408, DOI 10.4171/RMI/17
- Alan McIntosh and Yves Meyer, AlgĂšbres dâopĂ©rateurs dĂ©finis par des intĂ©grales singuliĂšres, C. R. Acad. Sci. Paris SĂ©r. I Math. 301 (1985), no. 8, 395â397 (French, with English summary). MR 808636
- 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. 24â68. MR 1013815, DOI 10.1007/BFb0086793
- Stephen W. Semmes, A criterion for the boundedness of singular integrals on hypersurfaces, Trans. Amer. Math. Soc. 311 (1989), no. 2, 501â513. MR 948198, DOI 10.1090/S0002-9947-1989-0948198-0
Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 110 (1990), 721-726
- MSC: Primary 42B20; Secondary 46E99, 47G10
- DOI: https://doi.org/10.1090/S0002-9939-1990-1028049-2
- MathSciNet review: 1028049