Bulletin (New Series) of the American Mathematical Society

Discrete analogues of singular Radon transforms

E. M. Stein and S. Wainger

Full-text: Open access

Article information

Bull. Amer. Math. Soc. (N.S.), Volume 23, Number 2 (1990), 537-544.

First available in Project Euclid: 4 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B20: Singular and oscillatory integrals (Calderón-Zygmund, etc.) 42B99: None of the above, but in this section 11L40: Estimates on character sums


Stein, E. M.; Wainger, S. Discrete analogues of singular Radon transforms. Bull. Amer. Math. Soc. (N.S.) 23 (1990), no. 2, 537--544. https://projecteuclid.org/euclid.bams/1183555909

Export citation


  • 1. G. I. Arkhipov and K. I. Oskolkov, On a special trigonometric series and its applications, Mat. Sb. 134(176) (1987), 147-158; Soviet Math 62 (1989), 145-156.
  • 2. J. Bourgain, On the maximal ergodic theorem for certain subsets of integers, Israel J. Math. 61 (1988), 39-72; 73-83.
  • 3. J. Bourgain, Return times of dynamical systems, Inst. Hautes Études Sci. preprint.
  • 4. L. Carleson, On the convergence and growth of partial sums of Fourier series, Acta Math. 116 (1966), 135-157.
  • 5. L. Carlitz and S. Uchiyama, Bounds for exponential sums, Duke Math. J. 24(1957), 37-41.
  • 6. D. Geller and E. M. Stein, Estimates for singular convolution operators on the Heisenberg group, Math. Ann. 267 (1984), 1-15.
  • 7. D. H. Phong and E. M. Stein, Hilbert integrals, singular integrals, and Radon transforms I, Acta Math. 157 (1986), 99-757.
  • 8. F. Ricci and E. M. Stein, Harmonic analysis on nilpotent groups and singular integrals, J. Funct. Anal. 73 (1987), 179-194; also 78 (1988), 56-84.
  • 9. P. Sjölin, Convergence almost everywhere of certain singular integrals and multiple Fourier series, Ark. Mat. 9 (1971), 65-90.
  • 10. E. M. Stein and S. Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), 1239-1295.
  • 11. I. Vinogradov, The method of trigonometrical sums in the theory of numbers, Interscience, New York, 1954.