Bilinear Operators with Non-Smooth Symbol, I

Journal of Fourier Analysis and Applications

Volumn 7, Issue 5, 2001, Pages 435-467

  Gilbert, John E ^a   Nahmod, Andrea R ^b  

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

^b UNIVERSITY OF MASSACHUSETTS   (United States)

Author keywords

Bilinear operator; Paraproduct; Singular multiplier; Wave packet

Indexed keywords

EID: 0345775324     PISSN: 10695869     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02511220     Document Type: Article

References (20)

1. Carleson, L. (1966). On convergence and growth of partial sums of Fourier series, Acta Math., 116, 135-157.
2. Coifman, R.R., Lions, P.L., Meyer, Y., and Semmes, S. (1993). Compensated compactness and Hardy spaces, J. Math Pures Appl., 72, 247-286.
3. Coifman, R.R. and Meyer, Y. (1978). Au delà des opérateurs pseudo-differentiels, Astérisque, 57, Société Mathématique de France.
4. Coifman, R.R. and Meyer, Y. (1975). On commutators of singular integrals and bilinear singular integrals, Trans. Am. Math. Soc., 212, 315-331.
5. Coifman, R.R. and Meyer, Y. (1991). Ondelettes et opérateurs III, Opérateurs Multilinéaires, Hermann, Ed., Paris.
6. Daubechies, I., Landau, H.J., and Landau, Z. (1995). Gabor time-frequency lattices and the Wexler-Raz identity, J. Fourier Anal. Appl., 1, 437-478.
7. Fefferman, C. (1973). Pointwise convergence of Fourier series, Ann. of Math., 98, 551-571.
8. Folland, G.B. (1989). Harmonic Analysis in Phase Space, Princeton University Press, Princeton, NJ.
9. Gilbert, J.E., Han, Y.S., Hogan, J.A., Lakey, J.D., Weiland, D., and Weiss, G. (1998). Calderón reproducing formula and frames with applications to singular integrals, preprint.
10. Gilbert, J.E. and Nahmod, A.R. (1999). Hardy spaces and a Walsh model for bilinear cone operators, Trans. Am. Math. Soc., 351, 3267-3300.
11. p-boundedness of time-frequency paraproducts, II, preprint, to appear in JFAA (Journal of Fourier Anal. Appl.).
12. Grafakos, L. and Torres, R.H. (1999). Multilinear Calderón-Zygmund theory, preprint.
13. Hogan, J.A. and Lakey, J.D. (1995). Extensions of the Heisenberg group by dilations and frames, Appl. Comp. Harm. Anal., 2, 174-199.
14. Kenig, C.E. and Stein, E.M. (1999). Multilinear estimates and fractional integration, Math. Research Lett., 6, 1-15.
15. p for 2/3 < p ≤ 1, Ann. of Math., 151(2), 35-57.
16. p estimates on the bilinear Hilbert transform, 2 < p < ∞, Ann. of Math., 146, 683-724.
17. Lacey, M. and Thiele, C. (1999). On Calderón's conjecture, Annals of Math., 149, 475-496.
18. Meyer, Y. (1990). Ondelettes et opérateurs. II, Opérateurs de Calderón-Zygmund, Hermann, Ed., Paris.
19. Muscalu, C., Tao, T., and Thiele, C. (1999). Multilinear operators given by singular multipliers, preprint.
20. Stein, E.M. (1993). Harmonic Analysis: Real Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton University Press, Princeton, NJ.