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arXiv · 2509.06474

A note on higher integrability of projections

Tuomas Orponen
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Abstract

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

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Tuomas Orponen. 2025-09-08. A note on higher integrability of projections. https://arxiv.org/abs/2509.06474

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