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Sharp Sobolev regularity of restricted X-ray transforms
Published online by Cambridge University Press: 30 August 2023
Abstract
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 $\mathbb {R}^3$.
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- Research Article
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- Copyright © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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