Journal d’Analyse Mathématique

, Volume 87, Issue 1, pp 187–198 | Cite as

Mixed norm estimates for a restricted X-ray transform

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References

  1. [1]
    J. Bourgain,Besicovitch type maximal operators and applications to Fourier analysis, Geom. Funct. Anal.1 (1991), 147–187.MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    M. Christ,Convolution, curvature, and combinatorics. A case study, Internat. Math. Res. Notices19 (1998), 1033–1048.CrossRefMathSciNetGoogle Scholar
  3. [3]
    M. B. Erdogan,Mixed norm estimates for a restricted X-ray transform in R4 and R5, Internat. Math. Res. Notices11 (2001), 575–600.CrossRefMathSciNetGoogle Scholar
  4. [4]
    A. Greenleaf and A. Seeger,Fourier integral operators with fold singularities, J. Reine Angew. Math.455 (1994), 35–56.MATHMathSciNetGoogle Scholar
  5. [5]
    A. Greenleaf and A. Seeger,Fourier integral operators with cusp singularities, Amer. J. Math.120 (1998), 1077–1119.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    A. Greenleaf and A. Seeger,On X-ray transforms for rigid line complexes and integrals over curves in R 4, Proc. Amer. Math. Soc.127 (1999), 3533–3545.MATHCrossRefMathSciNetGoogle Scholar
  7. [7]
    D. Oberlin,An estimate for a restricted X-ray transform, Canad. Math. Bull.43 (2000), 472–476.MATHMathSciNetGoogle Scholar
  8. [8]
    T. Tao and J. Wright,Lp improving estimates for averages along curves, preprint.Google Scholar
  9. [9]
    H. T. Wang,L p estimates for the X-ray transform restricted to line complexes of Kirillov type, Trans. Amer. Math. Soc.332 (1992), 793–821.MATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    T. Wolff,An improved bound for Kakeya type maximal functions, Rev. Mat. Iberoamericana11 (1995), 651–674.MATHMathSciNetGoogle Scholar
  11. [11]
    T. Wolff,A mixed norm estimate for the X-ray transform, Rev. Mat. Iberoamericana14 (1998), 561–601.MATHMathSciNetGoogle Scholar
  12. [12]
    T. Wolff,A sharp bilinear cone restriction estimate, Ann. of Math.153 (2001), 661–698.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 2002

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of CaliforniaBerkeleyUSA
  2. 2.Department of MathematicsCalifornia Institute of TechnologyPasadenaUSA

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