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arXiv · 1609.00168

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

Doowon Koh·Dongyoon Kwak
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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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Doowon Koh, Dongyoon Kwak. 2016-09-01. Sharp L^p-L^r estimates for k-plane transforms in finite fields. https://arxiv.org/abs/1609.00168

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