Sharp L^p-L^r estimates for k-plane transforms in finite fields

Abstract

We study mapping properties of finite field k-plane transforms. Using geometric combinatorics, we do an elaborate analysis to recover the critical endpoint estimate. As a consequence, we obtain optimal L^p-L^r estimates for all k-plane transforms in the finite field setting. In addition, applying Holder's inequality to our results, we obtain an estimate for multilinear k-plane transforms.

10 pages, no figure, abstract changed and a corollary added

References in corpus (1)

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