Sharp Sobolev regularity of restricted X-ray transforms

Hyerim Ko; Sanghyuk Lee; Sewook Oh

doi:10.1017/prm.2023.82

Sharp Sobolev regularity of restricted X-ray transforms

Hyerim Ko
, Sanghyuk Lee
, Sewook Oh

Department of Mathematics

Seoul National University
Korea Institute for Advanced Study

Research output: Contribution to journal › Journal article › peer-review

1 Scopus citations

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 R^d⁺¹, d ≽ 3.

Original language	English
Pages (from-to)	1583-1603
Number of pages	21
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	154
Issue number	5
DOIs	https://doi.org/10.1017/prm.2023.82
State	Published - 2024.10.1

Keywords

L Sobolev regularity

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10.1017/prm.2023.82

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title = "Sharp Sobolev regularity of restricted X-ray transforms",

abstract = "We study Lp-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 Lp-regularity estimates for the restricted X-ray transforms in Rd+1, d ≽ 3.",

keywords = "L Sobolev regularity",

author = "Hyerim Ko and Sanghyuk Lee and Sewook Oh",

note = "Publisher Copyright: {\textcopyright} The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.",

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AU - Ko, Hyerim

AU - Lee, Sanghyuk

AU - Oh, Sewook

N1 - Publisher Copyright: © The Author(s), 2023. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh.

PY - 2024/10/1

Y1 - 2024/10/1

N2 - We study Lp-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 Lp-regularity estimates for the restricted X-ray transforms in Rd+1, d ≽ 3.

AB - We study Lp-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 Lp-regularity estimates for the restricted X-ray transforms in Rd+1, d ≽ 3.

KW - L Sobolev regularity

UR - https://www.scopus.com/pages/publications/85170077773

U2 - 10.1017/prm.2023.82

DO - 10.1017/prm.2023.82

M3 - Journal article

AN - SCOPUS:85170077773

SN - 0308-2105

VL - 154

SP - 1583

EP - 1603

JO - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

JF - Proceedings of the Royal Society of Edinburgh Section A: Mathematics

IS - 5

ER -

Sharp Sobolev regularity of restricted X-ray transforms

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Keywords

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