关于 $4/3 < p < 2$ 的霍伦贝克-韦尔比茨基猜想

Vladan Jaguzović
{"title":"关于 $4/3 < p < 2$ 的霍伦贝克-韦尔比茨基猜想","authors":"Vladan Jaguzović","doi":"arxiv-2408.17093","DOIUrl":null,"url":null,"abstract":"Let \\(P_+\\) be the Riesz's projection operator and let \\(P_-=I-P_+.\\) We find\nbest estimates of the expression \\(\\left\\lVert \\left( \\left\\lvert P_+f\n\\right\\rvert ^s + \\left\\lvert P_-f \\right\\rvert ^s \\right) ^{1/s} \\right\\rVert\n_p \\) in terms of Lebesgue p-norm of the function \\(f \\in L^p(\\mathbf{T})\\) for\n\\(p \\in (4/3,2)\\) and \\(0 < s \\leq \\frac{p}{p-1},\\) thus extending results from\n\\cite{Melentijevic_2022} and \\cite{Melentijevic_2023}, where the mentioned\nrange is not considered.","PeriodicalId":501142,"journal":{"name":"arXiv - MATH - Complex Variables","volume":"2 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Hollenbeck-Verbitsky conjecture for $4/3 < p < 2$\",\"authors\":\"Vladan Jaguzović\",\"doi\":\"arxiv-2408.17093\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let \\\\(P_+\\\\) be the Riesz's projection operator and let \\\\(P_-=I-P_+.\\\\) We find\\nbest estimates of the expression \\\\(\\\\left\\\\lVert \\\\left( \\\\left\\\\lvert P_+f\\n\\\\right\\\\rvert ^s + \\\\left\\\\lvert P_-f \\\\right\\\\rvert ^s \\\\right) ^{1/s} \\\\right\\\\rVert\\n_p \\\\) in terms of Lebesgue p-norm of the function \\\\(f \\\\in L^p(\\\\mathbf{T})\\\\) for\\n\\\\(p \\\\in (4/3,2)\\\\) and \\\\(0 < s \\\\leq \\\\frac{p}{p-1},\\\\) thus extending results from\\n\\\\cite{Melentijevic_2022} and \\\\cite{Melentijevic_2023}, where the mentioned\\nrange is not considered.\",\"PeriodicalId\":501142,\"journal\":{\"name\":\"arXiv - MATH - Complex Variables\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-08-30\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Complex Variables\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2408.17093\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Complex Variables","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.17093","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

摘要

让(P_+)成为里兹投影算子,让(P_-=I-P_+.\)成为里兹投影算子。 我们可以找到表达式 \(left\lVert \left( \left\lvert P_+f\right\rvert ^s + \left\lvert P_-f \right\rvert ^s \right) ^{1/s} 的最佳估计值。\rightr Vert_p) in terms of Lebesgue p-norm of the function \(f \in L^p(\mathbf{T})\) for\(p \in (4/3,2)\) and \(0 < s \leq \frac{p}{p-1}、\)从而扩展了来自\cite{Melentijevic_2022}和\cite{Melentijevic_2023}的结果,在这两个结果中没有考虑提到的范围。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
On Hollenbeck-Verbitsky conjecture for $4/3 < p < 2$
Let \(P_+\) be the Riesz's projection operator and let \(P_-=I-P_+.\) We find best estimates of the expression \(\left\lVert \left( \left\lvert P_+f \right\rvert ^s + \left\lvert P_-f \right\rvert ^s \right) ^{1/s} \right\rVert _p \) in terms of Lebesgue p-norm of the function \(f \in L^p(\mathbf{T})\) for \(p \in (4/3,2)\) and \(0 < s \leq \frac{p}{p-1},\) thus extending results from \cite{Melentijevic_2022} and \cite{Melentijevic_2023}, where the mentioned range is not considered.
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
自引率
0.00%
发文量
0
期刊最新文献
Holomorphic approximation by polynomials with exponents restricted to a convex cone The Denjoy-Wolff Theorem in simply connected domains Best approximations for the weighted combination of the Cauchy--Szegö kernel and its derivative in the mean $L^2$-vanishing theorem and a conjecture of Kollár Nevanlinna Theory on Complete Kähler Connected Sums With Non-parabolic Ends
×
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
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 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 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1