Duke Mathematical Journal

$L^p$ estimates for Radon transforms in Euclidean and non-Euclidean spaces

Robert S. Strichartz

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Article information

Duke Math. J. Volume 48, Number 4 (1981), 699-727.

First available: 20 February 2004

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Primary: 43A85: Analysis on homogeneous spaces
Secondary: 22E30: Analysis on real and complex Lie groups [See also 33C80, 43-XX] 44A15: Special transforms (Legendre, Hilbert, etc.)


Strichartz, Robert S. L p estimates for Radon transforms in Euclidean and non-Euclidean spaces. Duke Mathematical Journal 48 (1981), no. 4, 699--727. doi:10.1215/S0012-7094-81-04839-0. http://projecteuclid.org/euclid.dmj/1077314927.

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  • [1] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc. 83 (1977), no. 4, 569–645.
  • [2] C. Fefferman and E. M. Stein, $H\spp$ spaces of several variables, Acta Math. 129 (1972), no. 3-4, 137–193.
  • [3] I. M. Gelfand, M. I. Graev, and N. Ya. Vilenkin, Generalized functions. Vol. 5, Academic Press [Harcourt Brace Jovanovich Publishers], New York, 1966 [1977].
  • [4] S. Helgason, Differential operators on homogenous spaces, Acta Math. 102 (1959), 239–299.
  • [5] S. Helgason, A duality for symmetric spaces with applications to group representations, Advances in Math. 5 (1970), 1–154 (1970).
  • [6] S. Helgason, The Radon transform, Progress in Mathematics, vol. 5, Birkhäuser Boston, Mass., 1980.
  • [7] R. A. Kunze and E. M. Stein, Uniformly bounded representations and harmonic analysis of the $2\times 2$ real unimodular group, Amer. J. Math. 82 (1960), 1–62.
  • [8] R. L. Lipsman, Uniformly bounded representations of the Lorentz groups, Amer. J. Math. 91 (1969), 938–962.
  • [9] F. Ricci and G. Weiss, A characterization of $H\sp1(\Sigma \sbn-1)$, Harmonic analysis in Euclidean spaces (Proc. Sympos. Pure Math., Williams Coll., Williamstown, Mass., 1978), Part 1, Proc. Sympos. Pure Math., XXXV, Part, Amer. Math. Soc., Providence, R.I., 1979, pp. 289–294.
  • [10] W. Rossmann, Analysis on real hyperbolic spaces, J. Funct. Anal. 30 (1978), no. 3, 448–477.
  • [11] V. I. Semjanistyi, On some integral transforms in Euclidean space, Soviet Math. Dokl. 1 (1960), 1114–1117.
  • [12]1 V. I. Semjanistyĭ, Homogeneous functions and some problems of integral geometry in the spaces of constant curvature, Soviet Math. Dokl. 2 (1961), 59–62.
  • [12]2 V. I. Semjanistyĭ, Some integral transformations and integral geometry in an elliptic space, Trudy Sem. Vektor. Tenzor. Anal. 12 (1963), 397–441.
  • [12]3 V. I. Semjanistyĭ, Certain problems of integral geometry in pseudo-Euclidean and non-Euclidean spaces, Trudy Sem. Vektor. Tenzor. Anal. 13 (1966), 244–302.
  • [13] K. T. Smith and D. C. Solmon, Lower dimensional integrability of $L\sp2$ functions, J. Math. Anal. Appl. 51 (1975), no. 3, 539–549.
  • [14] K. T. Smith, D. C. Solmon, and S. L. Wagner, Practical and mathematical aspects of the problem of reconstructing objects from radiographs, Bull. Amer. Math. Soc. 83 (1977), no. 6, 1227–1270.
  • [15] D. C. Solmon, The $X$-ray transform, J. Math. Anal. Appl. 56 (1976), no. 1, 61–83.
  • [16] D. C. Solmon, A note on $k$-plane integral transforms, J. Math. Anal. Appl. 71 (1979), no. 2, 351–358.
  • [17] R. J. Stanton and P. A. Tomas, Expansions for spherical functions on noncompact symmetric spaces, Acta Math. 140 (1978), no. 3-4, 251–276.
  • [18] E. M. Stein, The characterization of functions arising as potentials. II, Bull. Amer. Math. Soc. 68 (1962), 577–582.
  • [19] E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Mathematical Series, No. 30, Princeton University Press, Princeton, N.J., 1970.
  • [20] E. M. Stein and G. Weiss, Introduction to Fourier analysis on Euclidean spaces, Princeton University Press, Princeton, N.J., 1971.
  • [21] R. S. Strichartz, Convolutions with kernels having singularities on a sphere, Trans. Amer. Math. Soc. 148 (1970), 461–471.
  • [22] R. S. Strichartz, Harmonic analysis on hyperboloids, J. Functional Analysis 12 (1973), 341–383.
  • [23] R. S. Strichartz, The Hardy space $H\sp1$ on manifolds and submanifolds, Canad. J. Math. 24 (1972), 915–925.
  • [24] R. S. Strichartz, The explicit Fourier decomposition of $L\sp2(\rm SO(n)/\rm SO(n-m))$, Canad. J. Math. 27 (1975), 294–310.
  • [25] M. Sugiura, Representations of compact groups realized by spherical functions on symmetric spaces, Proc. Japan Acad. 38 (1962), 111–113.
  • [26] R. Takahashi, Sur les représentations unitaires des groupes de Lorentz généralisés, Bull. Soc. Math. France 91 (1963), 289–433.
  • [27] M. Takeuchi, Polynomial representations associated with symmetric bounded domains, Osaka J. Math. 10 (1973), 441–475.
  • [28] D. M. Oberlin and E. M. Stein, Mapping properties of the Radon transform, to appear Ind. Univ. Math. J.