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Sharp Sobolev regularity of restricted X-ray transforms
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 154 / Issue 5 / October 2024
- Published online by Cambridge University Press:
- 30 August 2023, pp. 1583-1603
- Print publication:
- October 2024
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- Article
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We study $L^p$
-Sobolev regularity estimates 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 $\mathbb {R}^3$
.
