曲线上平均值的平滑特性

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Hyerim Ko, Sanghyuk Lee, Sewook Oh
{"title":"曲线上平均值的平滑特性","authors":"Hyerim Ko, Sanghyuk Lee, Sewook Oh","doi":"10.1017/fmp.2023.2","DOIUrl":null,"url":null,"abstract":"Abstract We prove sharp smoothing properties of the averaging operator defined by convolution with a measure on a smooth nondegenerate curve \n$\\gamma $\n in \n$\\mathbb R^d$\n , \n$d\\ge 3$\n . Despite the simple geometric structure of such curves, the sharp smoothing estimates have remained largely unknown except for those in low dimensions. Devising a novel inductive strategy, we obtain the optimal \n$L^p$\n Sobolev regularity estimates, which settle the conjecture raised by Beltran–Guo–Hickman–Seeger [1]. Besides, we show the sharp local smoothing estimates on a range of p for every \n$d\\ge 3$\n . As a result, we establish, for the first time, nontrivial \n$L^p$\n boundedness of the maximal average over dilations of \n$\\gamma $\n for \n$d\\ge 4$\n .","PeriodicalId":2,"journal":{"name":"ACS Applied Bio Materials","volume":null,"pages":null},"PeriodicalIF":4.6000,"publicationDate":"2021-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":"{\"title\":\"Sharp smoothing properties of averages over curves\",\"authors\":\"Hyerim Ko, Sanghyuk Lee, Sewook Oh\",\"doi\":\"10.1017/fmp.2023.2\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We prove sharp smoothing properties of the averaging operator defined by convolution with a measure on a smooth nondegenerate curve \\n$\\\\gamma $\\n in \\n$\\\\mathbb R^d$\\n , \\n$d\\\\ge 3$\\n . Despite the simple geometric structure of such curves, the sharp smoothing estimates have remained largely unknown except for those in low dimensions. Devising a novel inductive strategy, we obtain the optimal \\n$L^p$\\n Sobolev regularity estimates, which settle the conjecture raised by Beltran–Guo–Hickman–Seeger [1]. Besides, we show the sharp local smoothing estimates on a range of p for every \\n$d\\\\ge 3$\\n . As a result, we establish, for the first time, nontrivial \\n$L^p$\\n boundedness of the maximal average over dilations of \\n$\\\\gamma $\\n for \\n$d\\\\ge 4$\\n .\",\"PeriodicalId\":2,\"journal\":{\"name\":\"ACS Applied Bio Materials\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.6000,\"publicationDate\":\"2021-05-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"9\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"ACS Applied Bio Materials\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/fmp.2023.2\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATERIALS SCIENCE, BIOMATERIALS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACS Applied Bio Materials","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/fmp.2023.2","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATERIALS SCIENCE, BIOMATERIALS","Score":null,"Total":0}
引用次数: 9

摘要

摘要我们在$\mathbb R^d$,$d\ge 3$中证明了由与光滑非退化曲线$\gamma$上的测度的卷积定义的平均算子的尖锐平滑性质。尽管这些曲线的几何结构很简单,但除了低维的平滑估计外,尖锐的平滑估计在很大程度上仍然未知。设计了一种新的归纳策略,得到了最优的$L^p$Sobolev正则性估计,解决了Beltran–Guo–Hickman–Seeger[1]提出的猜想。此外,我们还展示了每$d\ge3$在p范围内的尖锐局部平滑估计。因此,我们首次建立了$d\ge4$的$\gamma$的最大平均超扩张的非平凡$L^p$有界性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Sharp smoothing properties of averages over curves
Abstract We prove sharp smoothing properties of the averaging operator defined by convolution with a measure on a smooth nondegenerate curve $\gamma $ in $\mathbb R^d$ , $d\ge 3$ . Despite the simple geometric structure of such curves, the sharp smoothing estimates have remained largely unknown except for those in low dimensions. Devising a novel inductive strategy, we obtain the optimal $L^p$ Sobolev regularity estimates, which settle the conjecture raised by Beltran–Guo–Hickman–Seeger [1]. Besides, we show the sharp local smoothing estimates on a range of p for every $d\ge 3$ . As a result, we establish, for the first time, nontrivial $L^p$ boundedness of the maximal average over dilations of $\gamma $ for $d\ge 4$ .
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信