Hardy spaces and a Walsh model for bilinear cone operators

Transactions of the American Mathematical Society

Volumn 351, Issue 8, 1999, Pages 3267-3300

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

^a UNIVERSITY OF TEXAS AT AUSTIN   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 22644452497     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-99-02490-3     Document Type: Article

References (22)

1. J. Bergh and J. Löfström, Interpolation Spaces. An Introduction, Springer-Verlag, Berlin- Heidelberg-New York, 1976. MR 58:2349
2. J.-A. Chao, Lusin area functions on local fields, Pacific J. Math. 59 (1975), 383-390. MR 56:12771
3. J.-A. Chao, Hp-spaces of conjugate systems on local fields, Studia Math. 49 (1974), 267-287. MR 51:1292
4. 1-spaces dyadic martingales, Math. Ann. 240 (1979), 63-67. MR 80h:43002
5. 1 q-martingales, Pacific J. Math. 97 (1981), 307-317. MR 83k:60050
6. J.-A. Chao and M.H. Taibleson, A subregularity inequality of conjugate systems on local fields, Studia Math. 46 (1973), 249-257. MR 49:3459
7. R. R. Coifman, P. L. Lions, Y. Meyer and S. Semmes, Compensated compactness and Hardy spaces, J. Pure Math. Appl. 72 (1993), 247-286. MR 95d:46033
8. R. R. Coifman and Y. Meyer, Au delà des opérateurs pseudo-differentiels, Astérisque, Société Mathématique de France 57 (1978). MR 81b:47061
9. R. R. Coifman and Y. Meyer, On commutators of singular integrals and bilinear singular integrals, Trans. Amer. Math. Soc. 212 (1975), 315-331. MR 52:1144
10. 2(ℝ) ayant la structure du système de Walsh, preprint, Yale University, New Haven, CT, 1989.
11. R. R. Coifman, Y. Meyer and V. Wickerhauser, Size properties of wavelet-packets, Wavelets and Their Applications (M. B. Ruskai et al., eds.), Jones and Bartlett, Boston, 1992, pp. 453-470. MR 94a:42044
12. θq, Proc. Amer. Math. Soc. 44 (1974), 286-292. MR 50:10792
13. C. Fefferman, Pointwise convergence of Fourier series, Annals of Math. 98 (1973), 551-571. MR 49:5676; MR 98h:42004
14. R.F. Gundy, Martingale theory and pointwise convergence of certain orthogonal series, Trans. Amer. Math. Soc. 124 (1966), 228-248. MR 34:4802
15. E. Hernandez and G. Weiss, A first course on wavelets, CRC Press, Boca Raton, FL, 1996. MR 97i:42015
16. n, Math. Scand. 41 (1977), 140-152. MR 57:3729
17. S. Janson, On interpolation of multi-linear operators, Lecture Notes in Math., vol. 1302, Springer-Verlag, Berlin-Heidelberg-New York, 1988, pp. 290-302. MR 89g:46114
18. J.-P. Kahane and P. Lemarié-Rieusset, Fourier Series and Wavelets, Gordon and Breach, Amsterdam, 1995.
19. p estimates on the bilinear Hilbert transform, 2 p ∞, Annals of Math. 146 (1997), 683-724. MR 99b:42014
20. E.M. Stein, Topics in harmonic analysis related to the Littlewood-Paley theory, Ann. of Math. Studies No. 63, Princeton University Press, Princeton, NJ, 1970. MR 40:6176
21. E.M. Stein, Harmonic analysis: Real variable methods, orthogonality, and oscillatory integrals, Princeton University Press, Princeton, NJ, 1993. MR 40:6176
22. C.M. Thiele, Time-Frequency analysis in the Discrete Phase Plane, Thesis, Yale University, 1995, (available at http://www.math.yale.edu/pub/wavelets/papers/).