PreprintCC BY 4.0arXiv
A construction of Kakeya Sets in Arbitrary Dimension
Abstract
We construct Kakeya sets in arbitrary dimension d≥ 2, generalizing the classical Perron tree construction beyond dimension $2$. The Kakeya sets we construct have δ-neighbourhood of volume at most C|logδ|−(d−1), which improves on previously known constructions, and which is conjecturally optimal. We further derive consequences for the Lp-boundedness of radial Fourier multipliers in terms of Besov spaces with logarithmic smoothness.
Related
BibTeX
@misc{fernandezdelgado2026construction,
title = {{A construction of Kakeya Sets in Arbitrary Dimension}},
author = {Rafael J. Fernández-Delgado and Mikael de la Salle},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.14824},
eprint = {2607.14824},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.14824},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A construction of Kakeya Sets in Arbitrary Dimension
AU - Rafael J. Fernández-Delgado
AU - Mikael de la Salle
PY - 2026
DA - 2026/09/17
PB - arXiv
DO - 10.48550/arxiv.2607.14824
UR - https://arxiv.org/abs/2607.14824
AB - We construct Kakeya sets in arbitrary dimension d≥ 2, generalizing the classical Perron tree construction beyond dimension $2$. The Kakeya sets we construct have δ-neighbourhood of volume at most C|logδ|^−(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.
ER -