Acta Mathematica

The Newton polyhedron and oscillatory integral operators

D. H. Phong and E. M. Stein

Full-text: Open access

Note

Research supported in part by the National Science Foundation under Grants DMS-95-05399 and DMS-94-01579.A01.

Article information

Source
Acta Math., Volume 179, Number 1 (1997), 105-152.

Dates
Received: 28 June 1996
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.acta/1485891072

Digital Object Identifier
doi:10.1007/BF02392721

Mathematical Reviews number (MathSciNet)
MR1484770

Zentralblatt MATH identifier
0896.35147

Rights
1997 © Institut Mittag-Leffler

Citation

Phong, D. H.; Stein, E. M. The Newton polyhedron and oscillatory integral operators. Acta Math. 179 (1997), no. 1, 105--152. doi:10.1007/BF02392721. https://projecteuclid.org/euclid.acta/1485891072


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References

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