Uniform estimates for the X-ray transform restricted to polynomial curves

TL;DR

This paper derives near-optimal mixed-norm estimates for the X-ray transform along polynomial curves with weighted affine arclength, providing new insights even in well-curved scenarios.

Contribution

It introduces new bounds for the X-ray transform restricted to polynomial curves, depending only on dimension and polynomial degree, with some results novel in well-curved cases.

Findings

Established near-optimal mixed-norm estimates

Derived bounds depend only on dimension and polynomial degree

Some results are new even for well-curved curves

Abstract

We establish near-optimal mixed-norm estimates for the X-ray transform restricted to polynomial curves with a weight that is a power of the affine arclength. The bounds that we establish depend only on the spatial dimension and the degree of the polynomial. Some of our results are new even in the well-curved case.