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arXiv · 2508.19047

Furstenberg set theorem for transversal families of functions

Tuomas Orponen·Aleksi Pyörälä·Guangzeng Yi
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Abstract

We prove an extension of the Furstenberg set theorem to families of graphs satisfying a transversality condition. We apply the result to derive bounds on $L^{p}$-norms of Fourier transforms of fractal measures supported on plane curves.

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Tuomas Orponen, Aleksi Pyörälä, Guangzeng Yi. 2025-08-26. Furstenberg set theorem for transversal families of functions. https://arxiv.org/abs/2508.19047

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