Duke Mathematical Journal

Maximal functions and Fourier transforms

José L. Rubio de Francia

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 53, Number 2 (1986), 395-404.

First available in Project Euclid: 20 February 2004

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 42B15: Multipliers


Rubio de Francia, José L. Maximal functions and Fourier transforms. Duke Math. J. 53 (1986), no. 2, 395--404. doi:10.1215/S0012-7094-86-05324-X. http://projecteuclid.org/euclid.dmj/1077305049.

Export citation


  • [1] J. Bourgain, On the spherical maximal function in the plane, Preprint.
  • [2] J. García-Cuerva and J. L. Rubio de Francia, Weighted norm inequalities and related topics, North-Holland Mathematics Studies, vol. 116, North-Holland Publishing Co., Amsterdam, 1985.
  • [3] A. Greenleaf, Principal curvature and harmonic analysis, Indiana Univ. Math. J. 30 (1981), no. 4, 519–537.
  • [4] L. Hormander, Estimates for translation invariant operators in $L\spp$ spaces, Acta Math. 104 (1960), 93–140.
  • [5] J.L. Rubio de Francia, F. J. Ruiz, and J. L. Torrea, Calderón-Zygmund theory for operator-valued kernels, Adv. in Math. (1986), to appear.
  • [6] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970.
  • [7] E. M. Stein, Maximal functions. I. Spherical means, Proc. Nat. Acad. Sci. U.S.A. 73 (1976), no. 7, 2174–2175.
  • [8] C. D. Sogge and E. M. Stein, Averages of functions over hypersurfaces in $\bf R\sp n$, Invent. Math. 82 (1985), no. 3, 543–556.
  • [9] E. M. Stein and S. Wainger, Problems in harmonic analysis related to curvature, Bull. Amer. Math. Soc. 84 (1978), no. 6, 1239–1295.
  • [10] F. Zo, A note on approximation of the identity, Studia Math. 55 (1976), no. 2, 111–122.
  • [11] A. Carbery, The boundedness of the maximal Bochner-Riesz operator on $L\sp4(\bf R\sp2)$, Duke Math. J. 50 (1983), no. 2, 409–416.