Journal d’Analyse Mathématique

, Volume 54, Issue 1, pp 165–188 | Cite as

Averages over hypersurfaces smoothness of generalized Radon transforms

  • C. D. Sogge
  • E. M. Stein
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    L. Börjeson,Estimates of Bochner-Riesz operators and of averages over hypersurfaces, Thesis, Stockholm Univ., 1987.Google Scholar
  2. 2.
    J. Bourgain,Averages in the plane over convex curves and maximal operators, J. Analyse Math.47, (1986), 69–85.MATHMathSciNetCrossRefGoogle Scholar
  3. 3.
    A. Carbery,The boundedness of the maximal Bochner-Riesz operator on L 4(R2), Duke Math. J.50 (1983), 409–416.MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    L. Carleson and P. Sjölin,Oscillatory integrals and a multiplier problem for the disc, Studia Math.44 (1972), 287–299.MATHMathSciNetGoogle Scholar
  5. 5.
    F. M. Christ and C. D. SoggeThe weak type L 1 convergence of eigenfunction expansions for pdeudodifferential operators, Invent. Math.94 (1988), 421–453.MATHCrossRefMathSciNetGoogle Scholar
  6. 6.
    P. Constantin and J. Saut,Effets régularisants locaux pour des équations dispersives générales, C. R. Acad. Sci. Paris, Série I304 (1987), 407–410.MATHMathSciNetGoogle Scholar
  7. 7.
    K. J. Falconer,The Geometry of Fractal Sets, Cambridge Univ. Press, Cambridge, 1985.MATHGoogle Scholar
  8. 8.
    C. Fefferman and E. M. Stein,H p spaces of several variables, Acta Math.129 (1972), 137–193.MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    A. Greenleaf,Principal curvature and harmonic analysis, Indiana Math. J.30 (1982), 519–537.CrossRefMathSciNetGoogle Scholar
  10. 10.
    V. Guillemin and S. Sternberg,Geometric Asymptotics, Am. Math. Soc., Providence, R.I., 1977.MATHGoogle Scholar
  11. 11.
    L. Hörmander,The spectral function of an elliptic operator, Acta Math.88 (1968), 341–370.Google Scholar
  12. 12.
    L. Hörmander,Fourier integal operators, I, Acta Math.127 (1971), 79–183.MATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    L. Hörmander,Oscillatory integrals and multipliers on FL p, Ark. Mat.11 (1971), 1–11.CrossRefGoogle Scholar
  14. 14.
    L. Hörmander,The Analysis of Linear Partial Differential Operators III, Springer-Verlag, Berlin, 1985.MATHGoogle Scholar
  15. 15.
    M. Kaneko and G. Sunouchi,On the Littlewood-Paley and Marcinkiewicz functions in higher dimensions, Tôhoku Math. J.37 (1985), 343–365.MATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    W. Littman,Fourier transforms of surface-carried measures and differentiability of surface averages, Bull. Am. Math. Soc.69 (1973), 766–770.MathSciNetGoogle Scholar
  17. 17.
    D. M. Oberlin and E. M. Stein,Mapping properties of the Radon transform, Indiana Math. J.31 (1982), 641–650.MATHCrossRefMathSciNetGoogle Scholar
  18. 18.
    D. H. Phong and E. M. Stein,Hilbert integrals, singular integrals, and Radon transforms I, Acta Math.157 (1986), 99–157.MATHCrossRefMathSciNetGoogle Scholar
  19. 19.
    J. L. Rubio de Francia,Maximal functions and Fourier transforms, Duke Math. J.53 (1986), 395–404.MATHCrossRefMathSciNetGoogle Scholar
  20. 20.
    P. Sjölin,Re'egularity of solutions to the Schrödinger equation, Duke Math. J.55 (1987), 699–715.MATHCrossRefMathSciNetGoogle Scholar
  21. 21.
    C. D. Sogge,On the almost everywhere convergence to L p data for higher order hyperbolic operators, Proc. Am. Math. Soc.100 (1987), 99–103.MATHCrossRefMathSciNetGoogle Scholar
  22. 22.
    C. D. Sogge and E. M. Stein,Averages of functions, over hypersurfaces in R n, Invent. Math.,82 (1985), 543–556.MATHCrossRefMathSciNetGoogle Scholar
  23. 23.
    C. D. Sogge and E. M. Stein,Averages over hypersurfaces: II, Invent. Math.86 (1986), 233–242.MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    E. M. Stein,Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, N.J., 1971.Google Scholar
  25. 25.
    E. M. Stein,Maximal functions: spherical means, Proc. Natl. Acad. Sci. U.S.A.73 (1976), 2174–2175.MATHCrossRefGoogle Scholar
  26. 26.
    E. M. Stein,Oscillatory integrals in Fourier analysis, inBeijing Lectures in Harmonic Analysis Princeton Univ. Press, Princeton, N.J., 1986, pp. 307–356.Google Scholar
  27. 27.
    E. M. Stein and S. Wainger,Problems in harmonic analysis related to curvature, Bull. Am. Math. Soc.84 (1978), 1239–1295.MATHMathSciNetGoogle Scholar
  28. 28.
    E. M. Stein and G. Weiss,Introduction to Fourier Analysis on Euclidean Spaces, Princeton Univ. Press, Princeton, N.J., 1971.MATHGoogle Scholar
  29. 29.
    L. Vega,Schrödinger equations: pointwise convergence to the initial data, Proc. Am. Math. Soc.102 (1988), 874–878.MATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Hebrew University of Jerusalem 1990

Authors and Affiliations

  • C. D. Sogge
    • 1
  • E. M. Stein
    • 2
  1. 1.Department of MathematicsUniversity of ChicagoChicagoUSA
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA

Personalised recommendations