Trasformate di Radon e operatori di convoluzione su gruppi e algebre di Lie

  • Giancarlo Travaglini


The following is an expository paper concerning the relations between Radon transforms and convolution operators associated to singular measures. A quick review of the classical theorems is presented and a recent result of F. Ricci and the author in the framework of compact Lie groups and Lie algebras is outlined.


  1. [1]
    Christ, M.,Estimates for the k-plane transform, Indiana Univ. Math. J.33 (1984), 891–910.CrossRefMathSciNetMATHGoogle Scholar
  2. [2]
    Clerc, J.L.,Localisation des sommes de Riesz sur un groupe de Lie compact, Studia Math.,55 (1976), 21–26.MathSciNetMATHGoogle Scholar
  3. [3]
    Drury, S.W. eGuo, K.,Convolution estimates related to surfaces of half the ambient dimension, Math. Proc. Cambridge Philos. Soc.,110, (1991), 151–159.MathSciNetMATHCrossRefGoogle Scholar
  4. [4]
    Gel'fand, I. M. eShilov, G.E., Generalized functions, Academic Press, 1964.Google Scholar
  5. [5]
    Hörmander, L.,Estimates for translation invariant operators in L p spaces, Acta Math.,104 (1960), 93–139.CrossRefMathSciNetMATHGoogle Scholar
  6. [6]
    Oberlin, D.M. eStein, E.M.,Mapping properties of the Radon transform, Indiana Univ. Math. J.,31 (1982), 641–650.CrossRefMathSciNetMATHGoogle Scholar
  7. [7]
    Pan, Y.,A remark on convolution with measures supported on curves, Canad. Math. Bull.,36 (1993), 245–250.MathSciNetMATHGoogle Scholar
  8. [8]
    Ricci, F. eTravaglini, G.,L p-Lq estimates for orbital measures and Radon transforms on compact Lie groups and Lie algebras, J. Funct. Anal.,129 (1995), 132–147.CrossRefMathSciNetMATHGoogle Scholar
  9. [9]
    Stein, E. M., Singular integrals and differentiability properties of functions, Princeton University Press, 1970.Google Scholar

Copyright information

© Birkhäuser-Verlag 1995

Authors and Affiliations

  • Giancarlo Travaglini
    • 1
  1. 1.Dipartimento di MatematicaUniversità degli Studi di MilanoMilanoItalia

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