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

John Bueti

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

Combinatorics 2007-05-23 v2 Classical Analysis and ODEs

Authors: John Bueti

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 $1 \leq p \leq \frac{kn+k+1}{k(k+1)}$ and $1 \leq q \leq (n-k)p'$ .

Keywords

incidence bound k-planes finite fields Kakeya maximal function L^p boundedness

Cite

@article{arxiv.math/0609337,
  title  = {An incidence bound for $k$-planes in $F^n$ and a planar variant of the Kakeya maximal function},
  author = {John Bueti},
  journal= {arXiv preprint arXiv:math/0609337},
  year   = {2007}
}

Comments

34 pages, 2 figures; Revised introduction and expanded references

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

Abstract

Keywords

Cite

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