Duke Mathematical Journal

Singular Radon transforms and oscillatory integrals

D. H. Phong and E. M. Stein

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Article information

Source
Duke Math. J. Volume 58, Number 2 (1989), 347-369.

Dates
First available in Project Euclid: 20 February 2004

Permanent link to this document
http://projecteuclid.org/euclid.dmj/1077307529

Digital Object Identifier
doi:10.1215/S0012-7094-89-05816-X

Mathematical Reviews number (MathSciNet)
MR1016425

Zentralblatt MATH identifier
0738.42011

Subjects
Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.)
Secondary: 44A15: Special transforms (Legendre, Hilbert, etc.) 58G15

Citation

Phong, D. H.; Stein, E. M. Singular Radon transforms and oscillatory integrals. Duke Math. J. 58 (1989), no. 2, 347--369. doi:10.1215/S0012-7094-89-05816-X. http://projecteuclid.org/euclid.dmj/1077307529.


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References

  • [DJS] G. David, J.-L. Journé, and S. Semmes, Opérateurs de Calderón-Zygmund, fonctions para-accrétives et interpolation, Rev. Mat. Iberoamericana 1 (1985), no. 4, 1–56.
  • [FS] G. B. Folland and E. M. Stein, Hardy spaces on homogeneous groups, Mathematical Notes, vol. 28, Princeton University Press, Princeton, N.J., 1982.
  • [GU] A. Greenleaf and G. Uhlmann, Estimates for singular Radon transforms and pseudodifferential operators with singular symbols, preprint.
  • [NSW] A. Nagel, E. M. Stein, and S. Wainger, Hilbert transforms and maximal functions related to variable curves, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978), Part 1, Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 95–98.
  • [PS] D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals, and Radon transforms. I, Acta Math. 157 (1986), no. 1-2, 99–157.
  • [PS2] D. H. Phong and E. M. Stein, Some further classes of pseudodifferential and singular-integral operators arising in boundary value problems. I. Composition of operators, Amer. J. Math. 104 (1982), no. 1, 141–172.
  • [SS] C. D. Sogge and E. M. Stein, Averages over hypersurfaces III, Smoothness of generalized Radon transforms, preprint.
  • [W] S. Wainger, Averages and singular integrals over lower-dimensional sets, Beijing lectures in harmonic analysis (Beijing, 1984) ed. E. M. Stein, Ann. of Math. Stud., vol. 112, Princeton Univ. Press, Princeton, NJ, 1986, pp. 357–421.