Restricted Radon Transforms and Projections of Planar Sets

Canadian mathematical bulletin

Daniel M. Oberlin¹ 

[1] Department of Mathematics, Florida State University, Tallahassee, FL 32306, USA

关键词: rational curves;    extremal rays;   

DOI  :  10.4153/CMB-2011-064-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

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.

【 授权许可】

Unknown