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

2016/09/01 by Doowon Koh, Koh, Doowon, Dongyoon Kwak +1
Mathematics · Computer Science · #Advanced Harmonic Analysis Research #Cryptography and Residue Arithmetic #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1609.00168

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.

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