Hostname: page-component-78c5997874-t5tsf Total loading time: 0 Render date: 2024-11-10T06:39:07.417Z Has data issue: false hasContentIssue false
  • English
  • Français

An Estimate For a Restricted X-Ray Transform

Published online by Cambridge University Press:  20 November 2018

Daniel M. Oberlin
Daniel M. Oberlin*
Affiliation:
Department of Mathematics, Florida State University, Tallahassee, Florida 32306-4510, USA, e-mail: oberlin@math.fsu.edu
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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

44A15
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 43 , Issue 4 , 01 December 2000 , pp. 472 - 476
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), 223–238.Google Scholar
[C2] Christ, M., Convolution, curvature, and combinatorics: a case study. Internat.Math. Res. Notices 19 (1998), 1033–1048.Google Scholar
[GS] Greenleaf, A. and Seeger, A., Fourier integral operators with cusp singularities. Amer. J. Math. 120 (1998), 1077–1119.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), 3533–3545.Google Scholar
[M] McMichael, D., Damping oscillatory integrals with polynomial phase. Math. Scand. 73 (1993), 215–228.Google Scholar
[O1] Oberlin, D., Lp-Lq mapping properties of the Radon transform. Springer Lect.Notes in Math. 995 (1983), 95–102.Google Scholar
[O2] Oberlin, D., Convolution estimates for some measures on curves. Proc. Amer.Math. Soc. 99 (1987), 56–60.Google Scholar
[O3] Oberlin, D., A convolution estimate for a measure on a curve in ℝ4. Proc.Amer.Math. Soc. 125 (1997), 1355–1361.Google Scholar
[O4] Oberlin, D., A convolution estimate for a measure on a curve in ℝ4. II, Proc. Amer. Math. Soc. 127 (1999), 217–221.Google Scholar