Uniform estimates on multi-linear operators with modulation symmetry

Journal d'Analyse Mathematique

Volumn 88, Issue , 2002, Pages 255-309

  Muscalu, Camil ^a   Tao, Terence ^a   Thiele, Christoph ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0036942620     PISSN: 00217670     EISSN: 15658538     Source Type: Journal    
DOI: 10.1007/BF02786579     Document Type: Article

References (29)

1. C. Calderon, On commutators of singular integrals, Studia Math. 53 (1975), 139-174.
2. R. R. Coifman and Y. Meyer, On commutators of singular integrals and bilinear singular integrals, Trans. Amer. Math. Soc. 212 (1975), 315-331.
3. R. R. Coifman and Y. Meyer, Au delà des opérateurs pseudo-différentiels, Astérisque 57, Société Mathématique de France, Paris, 1978.
4. R. R. Coifman and Y. Meyer, Commutateurs d'integrales singulières et opérateurs multllinéaires, Ann. Inst. Fourier (Grenoble) 28 (1978), 177-202.
5. 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.), Lecture Notes in Math. 779, Springer-Verlag, Berlin, 1979, pp. 104-122.
6. R. R. Coifman and Y. Meyer, Nonlinear harmonic analysis, operator theory and P.D.E., Beijing Lectures in Analysis, Ann. of Math. Stud. 112 (1986), 3-46.
7. R. R. Coifman and Y. Meyer, Ondelettes et opérateurs III, Opérateurs multilinéaires, Actualités Mathématiques, Hermann, Paris, 1991.
8. C. Fefferman, Pointwise convergence of Fourier series, Ann. of Math. (2) 98 (1973), 551-571.
9. J. Gilbert and A. Nahmod, Hardy spaces and a Walsh model for bilinear cone operators, Trans. Amer. Math. Soc. 351 (1999), 3267-3300.
10. J. Gilbert and A. Nahmod, Bilinear operators with non-smooth symbol, J. Fourier Anal. Appl. 7 (2001), 435-467.
11. P-boundedness for time-frequency paraproducts, J. Fourier Anal. Appl. 8 (2002), 109-171.
12. L. Grafakos and X. Li, Uniform bounds for the bilinear Hilbert transforms, I., preprint.
13. L. Grafakos and R. Torres, R. On multilinear singular integrals, preprint.
14. S. Janson, On interpolation of multilinear operators, in Function Spaces and Applications (Lund 1986), Lecture Notes in Math, 1302, Springer, Berlin-New York, 1988.
15. C. Kenig and E. Stein, Multilinear estimates and fractional interpolation. Math. Res. Lett. 6 (1999), 1-15.
16. p estimates on the bilinear Hilbert transform for 2 < p < ∞, Ann. of Math. (2) 146 (1997), 693-724.
17. M. Lacey and C. Thiele, On Calderon's conjecture. Ann. of Math, (2) 149 (1999), 475-496.
18. M. Lacey and C. Thiele, A proof of boundedness of the Carleson operator, Math. Res. Lett. 7 (2000), 361-370.
19. X. Li, Uniform bounds for the bilinear Hilbert transforms, II., preprint.
20. C. Muscalu, T. Tao and C. Thiele, Multi-linear operators given by singular multipliers. J. Amer. Math. Soc. 15 (2002), 469-496.
21. C. Muscalu, T. Tao and C. Thiele, Uniform estimates on paraproducts, J. Analyse Math. 87 (2002), 369-384.
22. p estimates for the biest I. The Walsh case, preprint.
23. p estimates for the biest II. The Fourier case, preprint.
24. E. Stein, Harmonic Analysis; Real Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, 1993.
25. 2 functions, and applications to non-linear dispersive equations, Amer. J. Math. 123 (2001), 839-908.
26. C. Thiele, On the bilinear Hilbert transform, Habilitationsschrift, Universität Kiel, 1998.
27. C. Thiele, The quartile operator and almost everywhere convergence of Walsh-Fourier series, Trans. Amer. Math. Soc. 352 (2000), 5745-5766.
28. C. Thiele, A uniform estimate for the quartile operator, Rev. Mat. Iberoamericana 18 (2002), 115-134.
29. C. Thiele, A uniform estimate, Ann. of Math. (2) 157 (2002), 1-45.