Israel Journal of Mathematics

, Volume 15, Issue 1, pp 44–52 | Cite as

A note on spherical summation multipliers

  • Charles Fefferman


We give a new proof of a theorem of L. Carleson and P. Sjölin onL p -boundedness of spherical summation operators in two variables.


Restriction Theorem Maximal Function Convolution Operator Oscillatory Integral Multiplier Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    S. Bochner,Summation of multiple Fourier series by spherical means, Trans. Amer. Math. Soc. (1936).Google Scholar
  2. 2.
    L. Carleson and P. Sjölin,Oscillatory integrals and a multiplier problem for the disc, Studia Math, to appear.Google Scholar
  3. 3.
    C. Fefferman,Inequalities for strongly singular convolution operators, Acta Math. (1970).Google Scholar
  4. 4.
    C. Hefferman,The multiplier problem for the ball, Ann. of Math. (1972).Google Scholar
  5. 5.
    C. Herz,On the mean inversion of Fourier and Hankel transforms, Proc. Nat. Acad. Sci. U. S. A. (1954).Google Scholar
  6. 6.
    L. Hörmander,Oscillatory integrals and multipliers on FL p, to appear.Google Scholar
  7. 7.
    P. Sjölin, private communication.Google Scholar
  8. 8.
    E. M. Stein,Interpolation of linear operators, Trans. Amer. Math. Soc. (1956).Google Scholar
  9. 9.
    E. M. Stein and G. Weiss,Introduction to Fourier Analysis in Euclidean Spaces, Princeton University Press, 1971.Google Scholar

Copyright information

© Hebrew University 1973

Authors and Affiliations

  • Charles Fefferman
    • 1
  1. 1.Department of MathematicsUniversity of ChicagoChicagoU.S.A.

Personalised recommendations