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arXiv · 2607.14824

A construction of Kakeya Sets in Arbitrary Dimension

Rafael J. Fernández-Delgado·Mikael de la Salle
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Abstract

We construct Kakeya sets in arbitrary dimension $d\geq 2$, generalizing the classical Perron tree construction beyond dimension $2$. The Kakeya sets we construct have $\delta$-neighbourhood of volume at most $C|\log\delta|^{-(d-1)}$, which improves on previously known constructions, and which is conjecturally optimal. We further derive consequences for the $L^p$-boundedness of radial Fourier multipliers in terms of Besov spaces with logarithmic smoothness.

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BibTeXRIS

Rafael J. Fernández-Delgado, Mikael de la Salle. 2026-07-16. A construction of Kakeya Sets in Arbitrary Dimension. https://arxiv.org/abs/2607.14824

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