Two elementary proofs of the $L^ 2$ boundedness of Cauchy integrals on Lipschitz curves
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- by R. R. Coifman, Peter W. Jones and Stephen Semmes
- J. Amer. Math. Soc. 2 (1989), 553-564
- DOI: https://doi.org/10.1090/S0894-0347-1989-0986825-6
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References
- A.-P. Calderón, Cauchy integrals on Lipschitz curves and related operators, Proc. Nat. Acad. Sci. U.S.A. 74 (1977), no. 4, 1324–1327. MR 466568, DOI 10.1073/pnas.74.4.1324
- R. R. Coifman, A. McIntosh, and Y. Meyer, L’intégrale de Cauchy définit un opérateur borné sur $L^{2}$ pour les courbes lipschitziennes, Ann. of Math. (2) 116 (1982), no. 2, 361–387 (French). MR 672839, DOI 10.2307/2007065
- R. R. Coifman and R. Rochberg, Representation theorems for holomorphic and harmonic functions in $L^{p}$, Representation theorems for Hardy spaces, Astérisque, vol. 77, Soc. Math. France, Paris, 1980, pp. 11–66. MR 604369
- 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, DOI 10.24033/asens.1469
- Guy David and Jean-Lin Journé, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. (2) 120 (1984), no. 2, 371–397. MR 763911, DOI 10.2307/2006946
- 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, DOI 10.4171/RMI/17
- T. W. Gamelin, Wolff’s proof of the corona theorem, Israel J. Math. 37 (1980), no. 1-2, 113–119. MR 599306, DOI 10.1007/BF02762872
- 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, DOI 10.1007/BFb0086793 J. L. Journé, Calderón-Zygmund operators, pseudo-differential operators, and the Cauchy integral of Calderón, Lecture Notes in Math., no. 994, Springer-Verlag, Berlin and New York, 1983.
- Carlos E. Kenig, Weighted $H^{p}$ spaces on Lipschitz domains, Amer. J. Math. 102 (1980), no. 1, 129–163. MR 556889, DOI 10.2307/2374173
- 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
- Takafumi Murai, A real variable method for the Cauchy transform, and analytic capacity, Lecture Notes in Mathematics, vol. 1307, Springer-Verlag, Berlin, 1988. MR 944308, DOI 10.1007/BFb0078078
Bibliographic Information
- © Copyright 1989 American Mathematical Society
- Journal: J. Amer. Math. Soc. 2 (1989), 553-564
- MSC: Primary 42A50; Secondary 42B20, 47B38
- DOI: https://doi.org/10.1090/S0894-0347-1989-0986825-6
- MathSciNet review: 986825