Sharp L^p-L^r estimates for k-plane transforms in finite fields
Classical Analysis and ODEs
2017-02-14 v3
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.
Cite
@article{arxiv.1609.00168,
title = {Sharp L^p-L^r estimates for k-plane transforms in finite fields},
author = {Doowon Koh and Dongyoon Kwak},
journal= {arXiv preprint arXiv:1609.00168},
year = {2017}
}
Comments
10 pages, no figure, abstract changed and a corollary added