Duke Mathematical Journal

$L^2$ estimates for averaging operators along curves with two-sided $k$-fold singularities

Scipio Cuccagna

Full-text: Access denied (no subscription detected) We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Article information

Duke Math. J. Volume 89, Number 2 (1997), 203-216.

First available in Project Euclid: 19 February 2004

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Digital Object Identifier

Primary: 58G15
Secondary: 35S05: Pseudodifferential operators 47G30: Pseudodifferential operators [See also 35Sxx, 58Jxx]


Cuccagna, Scipio. L 2 estimates for averaging operators along curves with two-sided k -fold singularities. Duke Math. J. 89 (1997), no. 2, 203--216. doi:10.1215/S0012-7094-97-08910-9. http://projecteuclid.org/euclid.dmj/1077241015.

Export citation


  • [1] A. Greenleaf and A. Seeger, Fourier integral operators with fold singularities, J. Reine Angew. Math. 455 (1994), 35–56.
  • [2] L. Hörmander, Fourier integral operators. I, Acta Math. 127 (1971), no. 1-2, 79–183.
  • [3] L. Hörmander, The analysis of linear partial differential operators. IV, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 275, Springer-Verlag, Berlin, 1985.
  • [4] R. Melrose and M. Taylor, Near peak scattering and the corrected Kirchhoff approximation for a convex obstacle, Adv. in Math. 55 (1985), no. 3, 242–315.
  • [5] Y. Pan, Uniform estimates for oscillatory integral operators, J. Funct. Anal. 100 (1991), no. 1, 207–220.
  • [6] Y. Pan and C. D. Sogge, Oscillatory integrals associated to folding canonical relations, Colloq. Math. 60/61 (1990), no. 2, 413–419.
  • [7] D. H. Phong, Singular integrals and Fourier integral operators, Essays on Fourier analysis in honor of Elias M. Stein (Princeton, NJ, 1991) eds. C. Fefferman, R. Fefferman, and S. Wainger, Princeton Math. Ser., vol. 42, Princeton Univ. Press, Princeton, NJ, 1995, pp. 286–320.
  • [8] D. H. Phong and E. M. Stein, Radon transforms and torsion, Internat. Math. Res. Notices (1991), no. 4, 49–60.
  • [9] D. H. Phong and E. M. Stein, Oscillatory integrals with polynomial phases, Invent. Math. 110 (1992), no. 1, 39–62.
  • [10] D. H. Phong and E. M. Stein, Models of degenerate Fourier integral operators and Radon transforms, Ann. of Math. (2) 140 (1994), no. 3, 703–722.
  • [11] D. H. Phong and E. M. Stein, On a stopping process for oscillatory integrals, J. Geom. Anal. 4 (1994), no. 1, 105–120.
  • [12] D. H. Phong and E. M. Stein, Operator versions of the van der Corput lemma and Fourier integral operators, Math. Res. Lett. 1 (1994), no. 1, 27–33.
  • [13] A. Seeger, Degenerate Fourier integral operators in the plane, Duke Math. J. 71 (1993), no. 3, 685–745.
  • [14] A. Seeger, C. D. Sogge, and E. M. Stein, Regularity properties of Fourier integral operators, Ann. of Math. (2) 134 (1991), no. 2, 231–251.
  • [15] H. Smith and C. D. Sogge, $L\sp p$ regularity for the wave equation with strictly convex obstacles, Duke Math. J. 73 (1994), no. 1, 97–153.
  • [16] E. M. Stein, Harmonic Analysis: Real-Variable Methods, Orthogonality, and Oscillatory Integrals, Princeton Mathematical Series, vol. 43, Princeton University Press, Princeton, NJ, 1993.