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# Restricted Radon Transforms and Projections of Planar Sets

Published:2011-04-06
Printed: Dec 2012
• Daniel M. Oberlin,
Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA
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## Abstract

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.