Acta Mathematica

, Volume 179, Issue 1, pp 105–152 | Cite as

The Newton polyhedron and oscillatory integral operators

  • D. H. Phong
  • E. M. Stein
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Arnold, V., Varchenko, A. &Gussein-Zade, S.,Singularités des applications différentiables. Mir, Moscow, 1986.Google Scholar
  2. [2]
    Connor, J. L., Curtis, P. R. &Young, R. A. W., Uniform asymptotics of oscillating integrals: applications in chemical physics, inWave Asymptotics (Manchester, 1990), pp. 24–42. Cambridge Univ. Press, Cambridge, 1992.Google Scholar
  3. [3]
    Greenleaf, A. &Seeger, A., Fourier integral operators with fold singularities.J. Reine Angew. Math., 445 (1994), 35–56.MathSciNetGoogle Scholar
  4. [4]
    Greenleaf, A. &Uhlmann, G., Composition of some singular Fourier integral operators and estimates for the X-ray transform, I.Ann. Inst. Fourier, 40 (1990), 443–466; ILDuke Math. J., 64 (1991), 413–419.MATHMathSciNetGoogle Scholar
  5. [5]
    Hörmander, L., Oscillatory integrals and multipliers onFL p.Ark. Mat., 11 (1973), 1–11.MATHMathSciNetCrossRefGoogle Scholar
  6. [6]
    Kenig, C., Ponce, G. &Vega, L., Oscillatory integrals and regularity of wave equations.Indiana Math. J., 40 (1991), 33–69.MATHMathSciNetCrossRefGoogle Scholar
  7. [7]
    Ma, S., Forthcoming Ph.D. Thesis, Columbia University.Google Scholar
  8. [8]
    Melrose, R. &Taylor, M., Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle.Adv. in Math., 44 (1985), 242–315.MathSciNetCrossRefGoogle Scholar
  9. [9]
    Pan, Y. &Sogge, C., Oscillatory integrals associated with canonical folding relations.Colloq. Math., 40 (1990), 413–419.MathSciNetGoogle Scholar
  10. [10]
    Phong, D. H. &Stein, E. M., Radon transforms and torsion.Internat. Math. Res. Notices, 4 (1991), 49–60.MATHMathSciNetCrossRefGoogle Scholar
  11. [11]
    —, Oscillatory integrals with polynomial phases.Invent. Math., 110 (1992), 39–62.MATHMathSciNetCrossRefGoogle Scholar
  12. [12]
    —, Operator versions of the van der Corput lemma and Fourier integral operators.Math. Res. Lett., 1 (1994), 27–33.MATHMathSciNetGoogle Scholar
  13. [13]
    —, Models of degenerate Fourier integral operators and Radon transforms.Ann. of Math., 140 (1994), 703–722.MATHMathSciNetCrossRefGoogle Scholar
  14. [14]
    Saks, S. &Zygmund, A.,Analytic Functions. Elsevier, Amsterdam-London-New York, 1971.MATHGoogle Scholar
  15. [15]
    Seeger, A., Degenerate Fourier integral operators in the plane.Duke Math. J., 71 (1993), 685–745.MATHMathSciNetCrossRefGoogle Scholar
  16. [16]
    Siegel, C. L.,Complex Function Theory, Vol. I. Wiley-Interscience, New York, 1969.MATHGoogle Scholar
  17. [17]
    Taylor, M., Propagation, reflection, and diffraction of singularities of solutions to wave equations.Bull. Amer. Math. Soc., 84 (1978), 589–611.MATHMathSciNetCrossRefGoogle Scholar
  18. [18]
    Varchenko, A., Newton polyhedra and estimations of oscillatory integrals.Functional Anal. Appl., 18 (1976), 175–196.Google Scholar

Copyright information

© Institut Mittag-Leffler 1997

Authors and Affiliations

  • D. H. Phong
    • 1
  • E. M. Stein
    • 2
  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA
  2. 2.Department of MathematicsPrinceton UniversityPrincetonUSA

Personalised recommendations