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Bulletin of the American Mathematical Society

ISSN 1088-9485(online) ISSN 0273-0979(print)

 

 

Nonlinear Fourier analysis


Author: Stephen Semmes
Journal: Bull. Amer. Math. Soc. 20 (1989), 1-18
MSC (1985): Primary 42B99
MathSciNet review: 959211
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  • Jean-Michel Bony, Calcul symbolique et propagation des singularités pour les équations aux dérivées partielles non linéaires, Ann. Sci. École Norm. Sup. (4) 14 (1981), no. 2, 209–246 (French). MR 631751
  • A.-P. Calderón, Commutators of singular integral operators, Proc. Nat. Acad. Sci. U.S.A. 53 (1965), 1092–1099. MR 0177312
  • A.-P. Calderón, Algebras of singular integral operators, Singular integrals (Proc. Sympos. Pure Math., Chicago, Ill., 1966), Amer. Math. Soc., Providence, R.I., 1967, pp. 18–55. MR 0394309
  • 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 0466568
  • A.-P. Calderón, Commutators, singular integrals on Lipschitz curves and applications, Proceedings of the International Congress of Mathematicians (Helsinki, 1978), Acad. Sci. Fennica, Helsinki, 1980, pp. 85–96. MR 562599
  • Ronald R. Coifman and Yves Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque, vol. 57, Société Mathématique de France, Paris, 1978 (French). With an English summary. MR 518170
  • R. R. Coifman and Y. Meyer, Une généralisation du théorème de Calderón sur l’intégrale de Cauchy, Fourier analysis (Proc. Sem., El Escorial, 1979) Asoc. Mat. Espa nola, vol. 1, Asoc. Mat. Espa nola, Madrid, 1980, pp. 87–116 (French). MR 582251
  • [CM3] R. Coifman and Y. Meyer, Lavrentiev's curves and conformal mapping, Institut Mittag-Leffler, Report No. 5, 1983.
  • R. R. Coifman and Yves Meyer, Nonlinear harmonic analysis, operator theory and P.D.E, Beijing lectures in harmonic analysis (Beijing, 1984) Ann. of Math. Stud., vol. 112, Princeton Univ. Press, Princeton, NJ, 1986, pp. 3–45. MR 864370
  • R. R. Coifman, D. G. Deng, and Y. Meyer, Domaine de la racine carrée de certains opérateurs différentiels accrétifs, Ann. Inst. Fourier (Grenoble) 33 (1983), no. 2, x, 123–134 (French, with English summary). MR 699490
  • 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, 10.2307/2007065
  • [D] G. David, Thése de troisiéme cycle, Université de Paris XI, 91405 Orsay, France.
  • 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, 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, 10.4171/RMI/17
  • Eugene B. Fabes, David S. Jerison, and Carlos E. Kenig, Multilinear Littlewood-Paley estimates with applications to partial differential equations, Proc. Nat. Acad. Sci. U.S.A. 79 (1982), no. 18, 5746–5750. MR 674919
  • Eugene B. Fabes, David S. Jerison, and Carlos E. Kenig, Necessary and sufficient conditions for absolute continuity of elliptic-harmonic measure, Ann. of Math. (2) 119 (1984), no. 1, 121–141. MR 736563, 10.2307/2006966
  • Eugene B. Fabes, David S. Jerison, and Carlos E. Kenig, Multilinear square functions and partial differential equations, Amer. J. Math. 107 (1985), no. 6, 1325–1368 (1986). MR 815765, 10.2307/2374409
  • Carlos E. Kenig, Elliptic boundary value problems on Lipschitz domains, Beijing lectures in harmonic analysis (Beijing, 1984) Ann. of Math. Stud., vol. 112, Princeton Univ. Press, Princeton, NJ, 1986, pp. 131–183. MR 864372
  • C. Kenig and Y. Meyer, Kato’s square roots of accretive operators and Cauchy kernels on Lipschitz curves are the same, Recent progress in Fourier analysis (El Escorial, 1983) North-Holland Math. Stud., vol. 111, North-Holland, Amsterdam, 1985, pp. 123–143. MR 848144, 10.1016/S0304-0208(08)70282-2
  • P. G. Lemarié and Y. Meyer, Ondelettes et bases hilbertiennes, Rev. Mat. Iberoamericana 2 (1986), no. 1-2, 1–18 (French). MR 864650, 10.4171/RMI/22
  • [M1] Y. Meyer, Principe d'incertitude, bases hilbertiennes, et algèbres d'operateurs, Seminaire Bourbaki, Feb. 1986, no. 662.
  • Yves Meyer, Wavelets and operators, Analysis at Urbana, Vol. I (Urbana, IL, 1986–1987) London Math. Soc. Lecture Note Ser., vol. 137, Cambridge Univ. Press, Cambridge, 1989, pp. 256–365. MR 1009177
  • 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
  • Stephen W. Semmes, The Cauchy integral, chord-arc curves, and quasiconformal mappings, The Bieberbach conjecture (West Lafayette, Ind., 1985) Math. Surveys Monogr., vol. 21, Amer. Math. Soc., Providence, RI, 1986, pp. 167–183. MR 875240, 10.1090/surv/021/14
  • Jan-Olov Strömberg, A modified Franklin system and higher-order spline systems on 𝑅ⁿ as unconditional bases for Hardy spaces, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 475–494. MR 730086
  • E. M. Stein, The development of square functions in the work of A. Zygmund, Bull. Amer. Math. Soc. (N.S.) 7 (1982), no. 2, 359–376. MR 663787, 10.1090/S0273-0979-1982-15040-6
  • Elias M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory., Annals of Mathematics Studies, No. 63, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1970. MR 0252961

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DOI: http://dx.doi.org/10.1090/S0273-0979-1989-15681-4