A note on higher integrability of projections

Abstract

Let $t\in [1,2)$ and $p>2/(2-t)$. I construct a $t$-Frostman Borel measure $\hat{I}¼$ on $[0,1{]}^2$ such that $\ddot{I}{€}_{\hat{I}}¸\hat{I}¼\notin L^p$ for every $\hat{I}¸\in S^1$. This answers a question of Peres and Schlag.

8 pages, 3 figures. v2: reviewer comments taken into account, to appear in BLMS