An incidence bound for $k$-planes in $F^n$ and a planar variant of the Kakeya maximal function

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/116487We 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 $1 \leq p \leq \frac{kn+k+1}{k(k+1)}$ and $1 \leq q \leq (n-k)p'$.34 pages, 2 figures; Revised introduction and expanded referencesCombinatoricsClassical Analysis and ODEsAn incidence bound for $k$-planes in $F^n$ and a planar variant of the Kakeya maximal functiontext