Restricted Radon transforms and projections of planar sets

Abstract

We establish a mixed norm estimate for the Radon transform in the plane 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.

6 pages

Cited by in corpus (1)

• On the dimension of exceptional parameters for nonlinear projections, and the discretized Elekes-Rónyai theorem