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

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 $1\le p\le \frac{kn+k+1}{k(k+1)}$ and $1\le q\le (n-k)p^{\prime }$.

34 pages, 2 figures; Revised introduction and expanded references

References in corpus (1)

• Incidence theorems for pseudoflats

Cited by in corpus (1)

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