Duke Mathematical Journal

The Bochner-Riesz conjecture implies the restriction conjecture

Terence Tao

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Article information

Source
Duke Math. J. Volume 96, Number 2 (1999), 363-375.

Dates
First available in Project Euclid: 19 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077229137

Digital Object Identifier
doi:10.1215/S0012-7094-99-09610-2

Mathematical Reviews number (MathSciNet)
MR1666558

Zentralblatt MATH identifier
0980.42006

Subjects
Primary: 42B15: Multipliers

Citation

The Bochner-Riesz conjecture implies the restriction conjecture. Duke Math. J. 96 (1999), no. 2, 363--375. doi:10.1215/S0012-7094-99-09610-2. http://projecteuclid.org/euclid.dmj/1077229137.


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References

  • [1] J. Bourgain, Besicovitch type maximal operators and applications to Fourier analysis, Geom. Funct. Anal. 1 (1991), no. 2, 147–187.
  • [2] Jean Bourgain, Some new estimates on oscillatory integrals, Essays on Fourier analysis in honor of Elias M. Stein (Princeton, NJ, 1991), Princeton Math. Ser., vol. 42, Princeton Univ. Press, Princeton, NJ, 1995, pp. 83–112.
  • [3] Anthony Carbery, Restriction implies Bochner-Riesz for paraboloids, Math. Proc. Cambridge Philos. Soc. 111 (1992), no. 3, 525–529.
  • [4] Lennart Carleson and Per Sjölin, Oscillatory integrals and a multiplier problem for the disc, Studia Math. 44 (1972), 287–299. (errata insert).
  • [5] Michael Christ, On almost everywhere convergence of Bochner-Riesz means in higher dimensions, Proc. Amer. Math. Soc. 95 (1985), no. 1, 16–20.
  • [6] Michael Christ, Weak type endpoint bounds for Bochner-Riesz multipliers, Rev. Mat. Iberoamericana 3 (1987), no. 1, 25–31.
  • [7] Michael Christ, On the regularity of inverses of singular integral operators, Duke Math. J. 57 (1988), no. 2, 459–484.
  • [8] Michael Christ, Weak type $(1,1)$ bounds for rough operators, Ann. of Math. (2) 128 (1988), no. 1, 19–42.
  • [9] F. M. Christ and C. D. Sogge, The weak type $L\sp 1$ convergence of eigenfunction expansions for pseudodifferential operators, Invent. Math. 94 (1988), no. 2, 421–453.
  • [10] Antonio Cordoba, The Kakeya maximal function and the spherical summation multipliers, Amer. J. Math. 99 (1977), no. 1, 1–22.
  • [11] Charles Fefferman, Inequalities for strongly singular convolution operators, Acta Math. 124 (1970), 9–36.
  • [12] Charles Fefferman, The multiplier problem for the ball, Ann. of Math. (2) 94 (1971), 330–336.
  • [13] Charles Fefferman, A note on spherical summation multipliers, Israel J. Math. 15 (1973), 44–52.
  • [14] Lars Hörmander, Oscillatory integrals and multipliers on $FL\spp$, Ark. Mat. 11 (1973), 1–11.
  • [15] I. L. Hwang, The $L\sp 2$-boundedness of pseudodifferential operators, Trans. Amer. Math. Soc. 302 (1987), no. 1, 55–76.
  • [16] II, William P. Minicozzi and Christopher D. Sogge, Negative results for Nikodym maximal functions and related oscillatory integrals in curved space, Math. Res. Lett. 4 (1997), no. 2-3, 221–237.
  • [17] A. Moyua, A. Vargas, and L. Vega, Schrödinger maximal function and restriction properties of the Fourier transform, Internat. Math. Res. Notices (1996), no. 16, 793–815.
  • [18] Andreas Seeger, Endpoint estimates for multiplier transformations on compact manifolds, Indiana Univ. Math. J. 40 (1991), no. 2, 471–533.
  • [19] Andreas Seeger, Endpoint inequalities for Bochner-Riesz multipliers in the plane, Pacific J. Math. 174 (1996), no. 2, 543–553.
  • [20] Christopher D. Sogge, On the convergence of Riesz means on compact manifolds, Ann. of Math. (2) 126 (1987), no. 2, 439–447.
  • [21] Christopher D. Sogge, Propagation of singularities and maximal functions in the plane, Invent. Math. 104 (1991), no. 2, 349–376.
  • [22] Elias M. Stein, Harmonic analysis: real-variable methods, orthogonality, and oscillatory integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993.
  • [23] Elias M. Stein and Guido Weiss, Introduction to Fourier analysis on Euclidean spaces, vol. 32, Princeton University Press, Princeton, N.J., 1971.
  • [24] Terence Tao, Weak-type endpoint bounds for Riesz means, Proc. Amer. Math. Soc. 124 (1996), no. 9, 2797–2805.
  • [25] T. Tao, The weak-type endpoint Bochner-Riesz conjecture and related problems, to appear.
  • [26] Peter A. Tomas, A restriction theorem for the Fourier transform, Bull. Amer. Math. Soc. 81 (1975), 477–478.
  • [27] Thomas H. Wolff, Recent work on sharp estimates in second-order elliptic unique continuation problems, J. Geom. Anal. 3 (1993), no. 6, 621–650.
  • [28] Thomas Wolff, An improved bound for Kakeya type maximal functions, Rev. Mat. Iberoamericana 11 (1995), no. 3, 651–674.