Fourier analytic properties of Kakeya sets in finite fields
Abstract
Abstract We prove that a Kakeya set in a vector space over a finite field of size always supports a probability measure, whose Fourier transform is bounded by for all non‐zero frequencies. We show that this bound is sharp in all dimensions at least 2. In particular, this provides a Fourier analytic proof that a Kakeya set in dimension 2 has size at least (which is asymptotically sharp). We also establish analogous results for sets containing ‐planes in a given set of orientations.
Fields of Study & Subjects
Advanced Harmonic Analysis Research
advanced mathematical theories
Publication details
- Journal / source
- Bulletin of the London Mathematical Society
- Volume
- 58
- Issue
- 5
- Publication date
- 20 April 2026
- Language
- EN