Sharp endpoint estimates for the $X$-ray transform and the Radon transform in finite fields

TL;DR

This paper proves precise $L^p-L^r$ bounds for X-ray and Radon transforms in finite fields, advancing understanding of their behavior in discrete geometric settings.

Contribution

It provides sharp $L^p-L^r$ estimates for these transforms in finite fields, a significant improvement over previous bounds.

Findings

Established sharp $L^p-L^r$ estimates for X-ray transforms

Established sharp $L^p-L^r$ estimates for Radon transforms

Enhanced understanding of geometric transforms in finite fields

Abstract

This note establishes sharp $L^p-L^r$ estimates for $X$-ray transforms and Radon transforms in finite fields.