An incidence bound for k-planes in Fⁿ and a planar variant of the Kakeya maximal function

2006/09/12 by John Bueti, Bueti, John
Mathematics · #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #Combinatorics (math.CO) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical Approximation and Integration

paper · pdf · doi:10.48550/arxiv.math/0609337

openalex publication_date 2006/09/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We discuss a planar variant of the Kakeya maximal function in the setting of a vector space over a finite field. Using methods from incidence combinatorics, we demonstrate that the operator is bounded from L^p to L^q when 1 ≤ p ≤ (kn+k+1)/(k(k+1)) and 1 ≤ q ≤ (n-k)p'.

Citations

• An x-ray estimate in Rⁿ
• A recursive bound for a Kakeya-type maximal operator

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• Maximal and (m,ε)-Kakeya bounds over ℤ/Nℤ for general N
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• Finite field restriction estimates based on Kakeya maximal operator estimates