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An Estimate For a Restricted X-Ray Transform

Published online by Cambridge University Press:  20 November 2018

Daniel M. Oberlin*
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510, USA, e-mail: oberlin@math.fsu.edu
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Abstract

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This paper contains a geometric proof of an estimate for a restricted x-ray transform. The result complements one of A. Greenleaf and A. Seeger.

Keywords

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 2000

References

[B] Blei, R., Fractional Dimensions and Bounded Fractional Forms. Mem. Amer.Math. Soc. (331) 57(1985).Google Scholar
[C1] Christ, M., On the restriction of the Fourier transform to curves: endpoint results and the degenerate case. Trans. Amer.Math. Soc. 287 (1985), 223238.Google Scholar
[C2] Christ, M., Convolution, curvature, and combinatorics: a case study. Internat.Math. Res. Notices 19 (1998), 10331048.Google Scholar
[GS] Greenleaf, A. and Seeger, A., Fourier integral operators with cusp singularities. Amer. J. Math. 120 (1998), 10771119.Google Scholar
[GSW] Greenleaf, A., Seeger, A. and Wainger, S., On x-ray transforms for rigid line complexes and integrals over curves in ℝ4. Proc. Amer. Math. Soc. 127 (1999), 35333545.Google Scholar
[M] McMichael, D., Damping oscillatory integrals with polynomial phase. Math. Scand. 73 (1993), 215228.Google Scholar
[O1] Oberlin, D., Lp-Lq mapping properties of the Radon transform. Springer Lect.Notes in Math. 995 (1983), 95102.Google Scholar
[O2] Oberlin, D., Convolution estimates for some measures on curves. Proc. Amer.Math. Soc. 99 (1987), 5660.Google Scholar
[O3] Oberlin, D., A convolution estimate for a measure on a curve in ℝ4. Proc.Amer.Math. Soc. 125 (1997), 13551361.Google Scholar
[O4] Oberlin, D., A convolution estimate for a measure on a curve in ℝ4. II, Proc. Amer. Math. Soc. 127 (1999), 217221.Google Scholar