This note reveals non-integrability of projections for t-Frostman measures in L^p spaces, indicating fundamental constraints.
Let t ∈ [1,2) and $p > 2/(2 - t)$. I construct a t-Frostman Borel measure $μ$ on [0,1]² such that π_θμ∉ Lᵖ for every θ∈ S¹. This answers a question of Peres and Schlag.
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Tuomas Orponen (2025) studied this question.
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