  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 $1 \leq q \leq (n-k)p'$.

Combinatorics;Classical Analysis and ODEs