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

Authors
Type
Preprint
Publication Date
Oct 12, 2006
Submission Date
Sep 12, 2006
Identifiers
arXiv ID: math/0609337
Source
arXiv
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 $1 \leq p \leq \frac{kn+k+1}{k(k+1)}$ and $1 \leq q \leq (n-k)p'$.