关于分数奥立兹-哈代不等式

IF 1.2 3区 数学 Q1 MATHEMATICS
T.V. Anoop , Prosenjit Roy , Subhajit Roy
{"title":"关于分数奥立兹-哈代不等式","authors":"T.V. Anoop ,&nbsp;Prosenjit Roy ,&nbsp;Subhajit Roy","doi":"10.1016/j.jmaa.2024.128980","DOIUrl":null,"url":null,"abstract":"<div><div>We establish the weighted fractional Orlicz-Hardy inequalities for various Young functions satisfying the <span><math><msub><mrow><mo>△</mo></mrow><mrow><mn>2</mn></mrow></msub></math></span>-condition. Further, we identify the critical cases for such Young function and prove the weighted fractional Orlicz-Hardy inequalities with logarithmic correction. Moreover, we discuss the analogous results in the local case. In the process, for any Young function Φ satisfying the <span><math><msub><mrow><mo>△</mo></mrow><mrow><mn>2</mn></mrow></msub></math></span>-condition and for any <span><math><mi>Λ</mi><mo>&gt;</mo><mn>1</mn></math></span>, the following inequality is established<span><span><span><math><mi>Φ</mi><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>≤</mo><mi>λ</mi><mi>Φ</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>+</mo><mfrac><mrow><mi>C</mi><mo>(</mo><mi>Φ</mi><mo>,</mo><mi>Λ</mi><mo>)</mo></mrow><mrow><msup><mrow><mo>(</mo><mi>λ</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><msubsup><mrow><mi>p</mi></mrow><mrow><mi>Φ</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>−</mo><mn>1</mn></mrow></msup></mrow></mfrac><mi>Φ</mi><mo>(</mo><mi>b</mi><mo>)</mo><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace><mo>∀</mo><mspace></mspace><mi>a</mi><mo>,</mo><mi>b</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo><mspace></mspace><mo>∀</mo><mspace></mspace><mi>λ</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mi>Λ</mi><mo>]</mo><mo>,</mo></math></span></span></span> where <span><math><msubsup><mrow><mi>p</mi></mrow><mrow><mi>Φ</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>:</mo><mo>=</mo><mi>sup</mi><mo>⁡</mo><mo>{</mo><mi>t</mi><mi>φ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>/</mo><mi>Φ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>:</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>}</mo></math></span>, <em>φ</em> is the right derivatives of Φ and <span><math><mi>C</mi><mo>(</mo><mi>Φ</mi><mo>,</mo><mi>Λ</mi><mo>)</mo></math></span> is a positive constant that depends only on Φ and Λ.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128980"},"PeriodicalIF":1.2000,"publicationDate":"2024-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On fractional Orlicz-Hardy inequalities\",\"authors\":\"T.V. Anoop ,&nbsp;Prosenjit Roy ,&nbsp;Subhajit Roy\",\"doi\":\"10.1016/j.jmaa.2024.128980\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><div>We establish the weighted fractional Orlicz-Hardy inequalities for various Young functions satisfying the <span><math><msub><mrow><mo>△</mo></mrow><mrow><mn>2</mn></mrow></msub></math></span>-condition. Further, we identify the critical cases for such Young function and prove the weighted fractional Orlicz-Hardy inequalities with logarithmic correction. Moreover, we discuss the analogous results in the local case. In the process, for any Young function Φ satisfying the <span><math><msub><mrow><mo>△</mo></mrow><mrow><mn>2</mn></mrow></msub></math></span>-condition and for any <span><math><mi>Λ</mi><mo>&gt;</mo><mn>1</mn></math></span>, the following inequality is established<span><span><span><math><mi>Φ</mi><mo>(</mo><mi>a</mi><mo>+</mo><mi>b</mi><mo>)</mo><mo>≤</mo><mi>λ</mi><mi>Φ</mi><mo>(</mo><mi>a</mi><mo>)</mo><mo>+</mo><mfrac><mrow><mi>C</mi><mo>(</mo><mi>Φ</mi><mo>,</mo><mi>Λ</mi><mo>)</mo></mrow><mrow><msup><mrow><mo>(</mo><mi>λ</mi><mo>−</mo><mn>1</mn><mo>)</mo></mrow><mrow><msubsup><mrow><mi>p</mi></mrow><mrow><mi>Φ</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>−</mo><mn>1</mn></mrow></msup></mrow></mfrac><mi>Φ</mi><mo>(</mo><mi>b</mi><mo>)</mo><mo>,</mo><mspace></mspace><mspace></mspace><mspace></mspace><mo>∀</mo><mspace></mspace><mi>a</mi><mo>,</mo><mi>b</mi><mo>∈</mo><mo>[</mo><mn>0</mn><mo>,</mo><mo>∞</mo><mo>)</mo><mo>,</mo><mspace></mspace><mo>∀</mo><mspace></mspace><mi>λ</mi><mo>∈</mo><mo>(</mo><mn>1</mn><mo>,</mo><mi>Λ</mi><mo>]</mo><mo>,</mo></math></span></span></span> where <span><math><msubsup><mrow><mi>p</mi></mrow><mrow><mi>Φ</mi></mrow><mrow><mo>+</mo></mrow></msubsup><mo>:</mo><mo>=</mo><mi>sup</mi><mo>⁡</mo><mo>{</mo><mi>t</mi><mi>φ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>/</mo><mi>Φ</mi><mo>(</mo><mi>t</mi><mo>)</mo><mo>:</mo><mi>t</mi><mo>&gt;</mo><mn>0</mn><mo>}</mo></math></span>, <em>φ</em> is the right derivatives of Φ and <span><math><mi>C</mi><mo>(</mo><mi>Φ</mi><mo>,</mo><mi>Λ</mi><mo>)</mo></math></span> is a positive constant that depends only on Φ and Λ.</div></div>\",\"PeriodicalId\":50147,\"journal\":{\"name\":\"Journal of Mathematical Analysis and Applications\",\"volume\":\"543 2\",\"pages\":\"Article 128980\"},\"PeriodicalIF\":1.2000,\"publicationDate\":\"2024-10-22\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematical Analysis and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022247X24009028\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Analysis and Applications","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022247X24009028","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

我们为满足△2 条件的各种杨函数建立了加权分数奥立兹-哈代不等式。此外,我们还确定了此类杨函数的临界情况,并证明了带对数修正的加权分数奥立兹-哈代不等式。此外,我们还讨论了局部情况下的类似结果。在此过程中,对于满足△2 条件的任意 Young 函数 Φ 和任意Λ>1,建立了以下不等式Φ(a+b)≤λΦ(a)+C(Φ,Λ)(λ-1)Φ+-1Φ(b),∀a,b∈[0,∞),∀λ∈(1,Λ],其中Φ+:=sup{tΦ(t)/Φ(t):t>0},Φ是Φ的右导数,C(Φ,Λ)是只取决于Φ和Λ的正常数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On fractional Orlicz-Hardy inequalities
We establish the weighted fractional Orlicz-Hardy inequalities for various Young functions satisfying the 2-condition. Further, we identify the critical cases for such Young function and prove the weighted fractional Orlicz-Hardy inequalities with logarithmic correction. Moreover, we discuss the analogous results in the local case. In the process, for any Young function Φ satisfying the 2-condition and for any Λ>1, the following inequality is establishedΦ(a+b)λΦ(a)+C(Φ,Λ)(λ1)pΦ+1Φ(b),a,b[0,),λ(1,Λ], where pΦ+:=sup{tφ(t)/Φ(t):t>0}, φ is the right derivatives of Φ and C(Φ,Λ) is a positive constant that depends only on Φ and Λ.
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
CiteScore
2.50
自引率
7.70%
发文量
790
审稿时长
6 months
期刊介绍: The Journal of Mathematical Analysis and Applications presents papers that treat mathematical analysis and its numerous applications. The journal emphasizes articles devoted to the mathematical treatment of questions arising in physics, chemistry, biology, and engineering, particularly those that stress analytical aspects and novel problems and their solutions. Papers are sought which employ one or more of the following areas of classical analysis: • Analytic number theory • Functional analysis and operator theory • Real and harmonic analysis • Complex analysis • Numerical analysis • Applied mathematics • Partial differential equations • Dynamical systems • Control and Optimization • Probability • Mathematical biology • Combinatorics • Mathematical physics.
×
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