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Radon transform

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  • tmitsis <tmitsis@yahoo.com>
    Does anybody know how one can prove geometrically the sharp estimate $ | mathcal R chi_E |_3 lesssim | chi_E |_{3/2}$ for the maximal Radon transform $ mathcal
    Message 1 of 1 , Feb 1, 2003
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      Does anybody know how one can prove geometrically the sharp estimate
      $\|\mathcal R\chi_E\|_3\lesssim\|\chi_E\|_{3/2}$
      for the maximal Radon transform $\mathcal R$ (maximal averages over 2-
      planes) in $\mathbb R^3$? (no Fourier transform, no complex
      interpolation)

      A suitable variant of Bourgain's "bush" argument doesn't give the
      sharp bound and Cordoba's classical argument gives just an $L^2
      \rightarrow L^2$ bound.
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