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Inventiones mathematicae

, Volume 84, Issue 3, pp 541–561 | Cite as

Maximal and singular integral operators via Fourier transform estimates

  • Javier Duoandikoetxea
  • José L. Rubio de Francia
Article

Keywords

Fourier Fourier Transform Integral Operator Singular Integral Operator 
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.

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References

  1. 1.
    Calderón, A.P., Zygmund, A.: On singular integrals. Am. J. Math.78, 289–309 (1956)Google Scholar
  2. 2.
    Calderón, C.: Lacunary spherical means. Ill. J. Math.23, 476–484 (1979)Google Scholar
  3. 3.
    Chen, L.K.: On a singular integral (Preprint)Google Scholar
  4. 4.
    Christ, M., Duoandikoetxea, J., Rubio de Francia, J.L.: Maximal operators related to Radon transform and the Calderón-Zygmund method of rotations (To appear in Duke Math. J.)Google Scholar
  5. 5.
    Coifman, R., Weiss, G.: Analyse harmonique non commutative sur certains espaces homogènes. Lect. Notes Math.242. (1971)Google Scholar
  6. 6.
    Coifman, R., Weiss, G.: Review of the book Littlewood-Paley and multiplier theory. Bull. Am. Math. Soc.84, 242–250 (1978)Google Scholar
  7. 7.
    Fefferman, R.: A note on singular integrals. Proc. Am. Math. Soc.74, 266–270 (1979)Google Scholar
  8. 8.
    García-Cuerva, J., Rubio de Francia, J.L.: Weighted norm inequalities and related topics. Amsterdam: North-Holland: 1985Google Scholar
  9. 9.
    Greenleaf, A.: Principal curvature and harmonic analysis. Indiana Univ. Math. J.30, 519–537 (1981)Google Scholar
  10. 10.
    Jawerth, B.: Weighted inequalities for maximal operators: Linearization, localization and factorization (To appear in Am. J. Math.)Google Scholar
  11. 11.
    Kurtz, D.S.: Littlewood-Paley and multiplier theorems on weightedL p spaces. Trans. Am. Math. Soc.259, 235–254 (1980)Google Scholar
  12. 12.
    Littman, W.: Fourier transform of surface-carried measures and differentiability of surface averages. Bull. Am. Math. Soc.69, 766–770 (1963)Google Scholar
  13. 13.
    Nagel, A., Stein, E.M., Wainger, S.: Differentiation in lacunary directions. Proc. Natl. Acad. Sci. USA75, 1060–1062 (1978)Google Scholar
  14. 14.
    Nagel, A., Wainger, S.: Hilbert transform associated with plane curves. Trans. Am. Math. Soc.223, 235–252 (1976)Google Scholar
  15. 15.
    Rivière, N.: Singular integrals and multiplier operators. Ark. Mat.9, 243–278 (1971)Google Scholar
  16. 16.
    Stein, E.M.: Singular integrals and differentiability properties of functions. Princeton N.J.: Princeton University Press 1970Google Scholar
  17. 17.
    Stein, E.M.: Oscillatory integrals in Fourier analysis (Preprint)Google Scholar
  18. 18.
    Stein, E.M., Wainger, S.: Problems in harmonic analysis related to curvature. Bull. Am. Math. Soc.84, 1239–1295 (1978)Google Scholar
  19. 19.
    Weinberg, D.A.: The Hilbert transform and maximal function for approximately homogeneous curves. Trans. Am. Math. Soc.267, 295–306 (1981)Google Scholar
  20. 20.
    Zygmund, A.: Trigonometric series, I & II. London, New York: Cambridge University Press 1959Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Javier Duoandikoetxea
    • 1
  • José L. Rubio de Francia
    • 1
  1. 1.División de MatemáticasUniversidad AutónomaMadridSpain

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