A bilinear approach to cone multipliers I. Restriction estimates

Geometric and Functional Analysis

Volumn 10, Issue 1, 2000, Pages 185-215

  Tao, Terence ^a   Vargas, Ana ^b  

^a UNIVERSITY OF CALIFORNIA   (United States)

^b UNIVERSIDAD AUTÓNOMA DE MADRID   (Spain)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0034384186     PISSN: 1016443X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000390050006     Document Type: Article

References (22)

1. B. BARCELO, On the restriction of the Fourier transform to a conical surface, Trans. Amer. Math. Soc. 292 (1985), 321-333.
2. J. BERGH, J. LÖFSTROM, Interpolation Spaces, Grund. Math. Wiss. 223 Springer-Verlag, 1976.
3. J. BOURGAIN, Besicovitch-type maximal operators and applications to Fourier analysis, GAFA 1 (1991), 147-187.
4. 3, Springer Lecture Notes in Mathematics 1469 (1991), 179-191.
5. J. BOURGAIN, A remark on Schrodinger operators, Israel J. Math. 77 (1992), 1-16.
6. J. BOURGAIN, Estimates for cone multipliers, Operator Theory: Advances and Applications 77 (1995), 41-60.
7. J. BOURGAIN, Some new estimates on oscillatory integrals, Essays in Fourier Analysis in honor of E.M. Stein, Princeton University Press (1995), 83-112.
8. L. CARLESON, P. SJÖLIN, Oscillatory integrals and a multiplier problem for the disc, Studia Math. 44 (1972), 287-299.
9. M. CHRIST, On the regularity of inverses of singular integral operators, Duke Math. J. 57 (1988), 459-484.
10. p estimates for the x-ray transform, Ill. J. Math. 27 (1983), 125-129.
11. 2 bilinear estimates for wave equations, preprint.
12. L. HÖRMANDER, Fourier integral operators, Acta Math. 127 (1971), 79-183.
13. A. MOYUA, A. VARGAS, L. VEGA, Schrödinger Maximal Function and Restriction Properties of the Fourier transform, International Math. Research Notices 16 (1996).
14. 3, Duke Math. J., to appear.
15. M. SPIVAK, A Comprehensive Introduction to Differential Geometry, Vol. 1, Publish or Perish Inc., 1979. Second Edition.
16. E.M. STEIN, Harmonic Analysis, Princeton University Press, 1993.
17. T. TAO, The Bochner-Riesz conjecture implies the Restriction conjecture, Duke Math. J., to appear.
18. T. TAO, A. VARGAS, A bilinear approach to cone multipliers II. Applications, GAFA, in this issue.
19. T. TAO, A. VARGAS, L. VEGA, A bilinear approach to the restriction and Kakeya conjectures, J. Amer. Math. Soc. 11 (1998), 967-1000.
20. P. TOMAS, A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975), 477-478.
21. T.H. WOLFF, An improved bound for Kakeya type maximal functions, Revista Mat. Iberoamericana. 11 (1995), 651-674.
22. T.H. WOLFF, A mixed norm estimate for the x-ray transform, Revista Mat. Iberoamericana, to appear.