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arXiv · 2111.04339

Sharp Sobolev regularity of restricted X-ray transforms

Hyerim Ko·Sanghyuk Lee·Sewook Oh
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Abstract

We study $L^p$-Sobolev regularity estimate for the restricted X-ray transforms generated by nondegenerate curves. Making use of the inductive strategy in the recent work by the authors, we establish the sharp $L^p$-regularity estimates for the restricted X-ray transforms in $\mathbb R^{d+1}$, $d\ge 3$. This extends the result due to Pramanik and Seeger in $\mathbb R^3$ to every dimension.

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Hyerim Ko, Sanghyuk Lee, Sewook Oh. 2023-06-05. Sharp Sobolev regularity of restricted X-ray transforms. https://doi.org/10.1017/prm.2023.82

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