Carleson measures, trees, extrapolation, and T(b) theorems

Publicacions Matematiques

Volumn 46, Issue 2, 2002, Pages 257-325

  Auscher, P ^a   Hofmann, S ^b   Muscalu, C ^c   Tao, T ^c   Thiele, C ^c  

^a CNRS   (France)

^b UNIVERSITY OF MISSOURI   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Accretivity; BMO; Calder n Zygmund theory; Extrapolation; Haar wavelets; T(b) theorems

Indexed keywords

EID: 1842461225     PISSN: 02141493     EISSN: None     Source Type: Journal    
DOI: 10.5565/PUBLMAT_46202_01     Document Type: Review

References (60)

1. n, dedicated to the memory of Tosio Kato, J. Evol. Equ. 1(4) (2001), 361-385.
2. n, Ann. of Math. (2) (to appear).
3. P. AUSCHER, S. HOFMANN, J. L. LEWIS AND P. TCHAMITCHIAN, Extrapolation of Carleson measures and the analyticity of Kato's square-root operators, Acta Math. 187(2) (2001), 161-190.
4. P. AUSCHER AND P. TCHAMITCHIAN, Bases d'ondelettes sur les courbes corde-arc, noyau de Cauchy et espaces de Hardy associés, Rev. Mat. Iberoamericana 5(3-4) (1989), 139-170.
5. P. AUSCHER AND P. TCHAMITCHIAN, Square root problem for divergence operators and related topics, Astérisque 249 (1998), 172 pp.
6. J. BERGH AND J. LÖFSTRÖM, "Interpolation spaces. An introduction", Grundlehren der Mathematisehen Wissenschaften 223, Springer-Verlag, Berlin-New York, 1976.
7. G. BEYLKIN, R. R. COIFMAN AND V. ROKHLIN, Fast wavelet transforms and numerical algorithms. I, Comm. Pure Appl. Math. 44(2) (1991), 141-183.
8. C. J. BISHOP, L. CARLESON, J. B. GARNETT AND P. W. JONES, Harmonic measures supported on curves, Pacific J. Math. 138(2) (1989), 233-236.
9. C. P. CALDERÓN, On commutators of singular integrals, Studia Math. 53(2) (1975), 139-174.
10. L. CARLESON, Lennart On convergence and growth of partial sumas of Fourier series, Acta Math. 116 (1966), 135-157.
11. M. CHRIST, A T(b) theorem with remarks on analytic capacity and the Cauchy integral, Colloq. Math. 60/61(2) (1990), 601-628.
12. M. CHRIST AND J.-L. JOURNÉ, Polynomial growth estimates for multilinear singular integral operators, Acta Math. 159(1-2) (1987), 51-80.
13. 2 pour les courbes lipschitziennes, Ann. of Math. (2) 116(2) (1982), 361-387.
14. R. R. COIFMAN AND Y. MEYER, On commutators of singular integrals and bilinear singular integrals, Trans. Amer. Math. Soc. 212 (1975), 315-331.
15. R. R. COIFMAN AND Y. MEYER, Commutateurs d'intégrales singulières et opérateurs multilinéaires, Ann. Inst. Fourier (Grenoble) 28(3) (1978), 177-202.
16. R. R. COIFMAN AND Y. MEYER, Fourier analysis of multilinear convolutions, Calderón's theorem, and analysis of Lipschitz curves, in: "Euclidean harmonic analysis" (Proc. Sem., Univ. Maryland, College Park, Md., 1979), Lecture Notes in Math. 779, Springer, Berlin, 1980, pp. 104-122.
17. R. R. COIFMAN AND Y. MEYER, Fourier analysis of multilinear convolutions, Calderón's theorem, and analysis of Lipschitz curves, in: "Euclidean harmonic analysis" (Proc. Sem., Univ. Maryland, College Park, Md., 1979), Lecture Notes in Math. 779, Springer, Berlin, 1980, pp. 104-122.
18. R. R. COIFMAN AND Y. MEYER, Au delà des opérateurs pseudodifférentiels, Astérisque 57 (1978), 185 pp.
19. R. R. COIFMAN AND Y. MEYER, Nonlinear harmonic analysis, operator theory and P.D.E., in: "Beijing lectures in harmonic analysis" (Beijing, 1984), Ann. of Math. Stud. 112, Princeton Univ. Press, Princeton, NJ, 1986, pp. 3-45.
20. R. R. COIFMAN AND Y. MEYER, Nonlinear harmonic analysis, operator theory and P.D.E., in: "Beijing lectures in harmonic analysis" (Beijing, 1984), Ann. of Math. Stud. 112, Princeton Univ. Press, Princeton, NJ, 1986, pp. 3-45.
21. R. R. COIFMAN AND Y. MEYER, "Ondelettes et opérateurs. III. Opérateurs multilinéaires", Actualités Mathématiques, Hermann, Paris, 1991.
22. 2 boundedness of Cauchy integrals on Lipschitz curves, J. Amer. Math. Soc. 2(3) (1989), 553-564.
23. G. DAVID, "Wavelets and singular integrals on curves and surfaces", Lecture Notes in Mathematics 1465, Springer-Verlag, Berlin, 1991.
24. G. DAVID AND J.-L. JOURNÉ, A boundedness criterion for generalized Calderón-Zygmund operators, Ann. of Math. (2) 120(2) (1984), 371-397.
25. G. DAVID, J.-L. JOURNÉ AND S. SEMMES, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1(4) (1985), 1-56.
26. G. DAVID AND S. SEMMES, "Analysis of and on uniformly rectifiable sets", Mathematical Surveys and Monographs 38, American Mathematical Society, Providence, RI, 1993.
27. C. FEFFERMAN, Pointwise convergence of Fourier series, Ann. of Math. (2) 98 (1973), 551-571.
28. C. FEFFERMAN AND E. M. STEIN, Some maximal inequalities, Amer. J. Math. 93 (1971), 107-115.
29. p spaces of several variables, Acta Math. 129(3-4) (1972), 137-193.
30. R. A. FEFFERMAN, C. E. KENIG AND J. PIPHER, The theory of weights and the Dirichlet problem for elliptic equations, Ann. of Math. (2) 134(1) (1991), 65-124.
31. J. B. GARNETT AND P. W. JONES, BMO from dyadic BMO, Pacific J. Math. 99(2) (1982), 351-371.
32. L. GRAFAKOS AND N. J. KALTON, The Marcinkiewicz multiplier condition for bilinear operators, Studia Math. 146(2) (2001), 115-156.
33. S. HOFMANN, M. LACEY AND A. MCINTOSH, The solution of the Kato problem for divergence form elliptic operators with Gaussian heat kernel bounds, Ann. of Math. (2) (to appear).
34. S. HOFMANN AND J. L. LEWIS, The Dirichlet problem for parabolic operators with singular drift terms, Mem. Amer. Math. Soc. 151(719) (2001), 113 pp.
35. S. JANSON, On interpolation of multilinear operators, in: "Function spaces and applications" (Lund, 1986), Lecture Notes in Math. 1302, Springer, Berlin, 1988, pp. 290-302.
36. S. JANSON, On interpolation of multilinear operators, in: "Function spaces and applications" (Lund, 1986), Lecture Notes in Math. 1302, Springer, Berlin, 1988, pp. 290-302.
37. F. JOHN, Quasi-isometric mappings, in: "Seminari 1962/63 Anal. Alg. Geom. e Topol.", vol. 2, Ist. Naz. Alta Mat., Ediz. Cremonese, Rome, 1965, pp. 462-473.
38. P. W. JONES, Square functions, Cauchy integrals, analytic capacity, and harmonic measure, in: "Harmonic analysis and partial differential equations" (El Escorial, 1987), Lecture Notes in Math. 1384, Springer, Berlin, 1989, pp. 24-68.
39. P. W. JONES, Square functions, Cauchy integrals, analytic capacity, and harmonic measure, in: "Harmonic analysis and partial differential equations" (El Escorial, 1987), Lecture Notes in Math. 1384, Springer, Berlin, 1989, pp. 24-68.
40. P. W. JONES, Rectifiable sets and the traveling salesman problem, Invent. Math. 102(1) (1990), 1-15.
41. N. H. KATZ, Maximal operators over arbitrary sets of directions, Duke Math. J. 97(1) (1999), 67-79.
42. N. H. KATZ, Remarks on maximal operators over arbitrary sets of directions, Bull. London Math. Soc. 31(6) (1999), 700-710.
43. p estimates on the bilinear Hilbert transform for 2 < p < ∞, Ann. of Math. (2) 146(3) (1997), 693-724.
44. M. LACEY AND C. THIELE, On Calderón's conjecture, Ann. of Math. (2) 149(2) (1999), 475-496.
45. M. LACEY AND C. THIELE, A proof of boundedness of the Carleson operator, Math. Res. Lett. 7(4) (2000), 361-370.
46. J. L. LEWIS AND M. A. M. MURRAY, The method of layer potentials for the heat equation in time-varying domains, Mem. Amer. Math. Soc. 114(545) (1995), 157 pp.
47. A. MCINTOSH AND Y. MEYER, Algèbres d'opérateurs définis par des intégrales singulières, C. R. Acad. Sci. Paris Sér. I Math. 301(8) (1985), 395-397.
48. Y. MEYER, "Ondelettes et opérateurs. I. Ondelettes", Actualités Mathématiques, Hermann, Paris, 1990.
49. C. MUSCALU, T. TAO AND C. THIELE, Multi-linear operators given by singular multipliers, J. Amer. Math. Soc. 15(2) (2002), 469-496 (electronic).
50. p estimates for the "biest", submitted to Math. Ann.
51. F. NAZAROV, S. TREIL AND A. VOLBERG, Accretive system Tb theorems on nonhomogeneous spaces, Duke Math. J. (to appear).
52. F. NAZAROV, S. TREIL AND A. VOLBERG, Tb theorems on nonhomogeneous spaces, Acta Math. (to appear).
53. M. C. PEREYRA, Lecture notes on dyadic harmonic analysis, in: "Second Summer School in Analysis and Mathematical Physics" (Cuernavaca, 2000), Contemp. Math. 289, Amer. Math. Soc., Providence, RI, 2001, pp. 1-60
54. M. C. PEREYRA, Lecture notes on dyadic harmonic analysis, in: "Second Summer School in Analysis and Mathematical Physics" (Cuernavaca, 2000), Contemp. Math. 289, Amer. Math. Soc., Providence, RI, 2001, pp. 1-60.
55. S. SEMMES, Square function estimates and the T(b) theorem, Proc. Amer. Math. Soc. 110(3) (1990), 721-726.
56. E. M. STEIN, "Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals", Princeton Mathematical Series 43, Monographs in Harmonic Analysis III, Princeton University Press, Princeton, NJ, 1993.
57. C. THIELE, Time-frequency analysis in the discrete phase plane, in: "Topics in analysis and its applications", World Sci. Publishing, River Edge, NJ, 2000, pp. 99-152.
58. C. THIELE, On the Bilinear Hilbert transform, Universität Kiel, Habilitationsschrift (1998).
59. 2 boundedness of the Cauchy integral and Menger curvature, in: "Harmonic analysis and boundary value problems" (Fayetteville, AR, 2000), Contemp. Math. 277, Amer. Math. Soc., Providence, RI, 2001, pp. 139-158.
60. 2 boundedness of the Cauchy integral and Menger curvature, in: "Harmonic analysis and boundary value problems" (Fayetteville, AR, 2000), Contemp. Math. 277, Amer. Math. Soc., Providence, RI, 2001, pp. 139-158.