Sharp Sobolev regularity of restricted X-ray transforms

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.

arXiv comment18 pages

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