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Restricted Radon Transforms and Projections of Planar Sets

Published online by Cambridge University Press:  20 November 2018

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

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We establish a mixed norm estimate for the Radon transform in ${{\mathbb{R}}^{2}}$ when the set of directions has fractional dimension. This estimate is used to prove a result about an exceptional set of directions connected with projections of planar sets. That leads to a conjecture analogous to a well-known conjecture of Furstenberg.

Keywords

44A1228A78
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 55 , Issue 4 , 01 December 2012 , pp. 815 - 820
Copyright
Copyright © Canadian Mathematical Society 2012

References

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