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

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

2006-09-12

arxiv.org/abs/math/0609337v2

Mathematics

Combinatorics

34 pages, 2 figures; Revised introduction and expanded references

Scientific paper

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

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