与拉盖尔多项式展开相关的哈代空间的最大函数表征

IF 0.7 2区 数学 Q2 MATHEMATICS
Jorge J. Betancor, Estefanía Dalmasso, Pablo Quijano, Roberto Scotto
{"title":"与拉盖尔多项式展开相关的哈代空间的最大函数表征","authors":"Jorge J. Betancor, Estefanía Dalmasso, Pablo Quijano, Roberto Scotto","doi":"10.1007/s13348-024-00433-z","DOIUrl":null,"url":null,"abstract":"<p>In this paper we introduce the atomic Hardy space <span>\\(\\mathcal {H}^1((0,\\infty ),\\gamma _\\alpha )\\)</span> associated with the non-doubling probability measure <span>\\(d\\gamma _\\alpha (x)=\\frac{2x^{2\\alpha +1}}{\\Gamma (\\alpha +1)}e^{-x^2}dx\\)</span> on <span>\\((0,\\infty )\\)</span>, for <span>\\({\\alpha &gt;-\\frac{1}{2}}\\)</span>. We obtain characterizations of <span>\\(\\mathcal {H}^1((0,\\infty ),\\gamma _\\alpha )\\)</span> by using two local maximal functions. We also prove that the truncated maximal function defined through the heat semigroup generated by the Laguerre differential operator is bounded from <span>\\(\\mathcal {H}^1((0,\\infty ),\\gamma _\\alpha )\\)</span> into <span>\\(L^1((0,\\infty ),\\gamma _\\alpha )\\)</span>.</p>","PeriodicalId":50993,"journal":{"name":"Collectanea Mathematica","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-03-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Maximal function characterization of Hardy spaces related to Laguerre polynomial expansions\",\"authors\":\"Jorge J. Betancor, Estefanía Dalmasso, Pablo Quijano, Roberto Scotto\",\"doi\":\"10.1007/s13348-024-00433-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper we introduce the atomic Hardy space <span>\\\\(\\\\mathcal {H}^1((0,\\\\infty ),\\\\gamma _\\\\alpha )\\\\)</span> associated with the non-doubling probability measure <span>\\\\(d\\\\gamma _\\\\alpha (x)=\\\\frac{2x^{2\\\\alpha +1}}{\\\\Gamma (\\\\alpha +1)}e^{-x^2}dx\\\\)</span> on <span>\\\\((0,\\\\infty )\\\\)</span>, for <span>\\\\({\\\\alpha &gt;-\\\\frac{1}{2}}\\\\)</span>. We obtain characterizations of <span>\\\\(\\\\mathcal {H}^1((0,\\\\infty ),\\\\gamma _\\\\alpha )\\\\)</span> by using two local maximal functions. We also prove that the truncated maximal function defined through the heat semigroup generated by the Laguerre differential operator is bounded from <span>\\\\(\\\\mathcal {H}^1((0,\\\\infty ),\\\\gamma _\\\\alpha )\\\\)</span> into <span>\\\\(L^1((0,\\\\infty ),\\\\gamma _\\\\alpha )\\\\)</span>.</p>\",\"PeriodicalId\":50993,\"journal\":{\"name\":\"Collectanea Mathematica\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2024-03-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Collectanea Mathematica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s13348-024-00433-z\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Collectanea Mathematica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s13348-024-00433-z","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0

摘要

在本文中,我们引入了原子哈代空间(mathcal {H}^1((0,\infty )、\d\gamma _\alpha (x)=\frac{2x^{2\alpha +1}}\{Gamma (\alpha +1)}e^{-x^2}dx\) on \((0,\infty )\), for \({\alpha >;-\)。通过使用两个局部最大函数,我们得到了 \(mathcal {H}^1((0,\infty ),\gamma _\alpha )\) 的特征。我们还证明了通过拉盖尔微分算子产生的热半群定义的截断最大函数从\(\mathcal {H}^1((0,\infty ),\gamma _\alpha ))到\(L^1((0,\infty ),\gamma _\alpha ))是有界的。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Maximal function characterization of Hardy spaces related to Laguerre polynomial expansions

In this paper we introduce the atomic Hardy space \(\mathcal {H}^1((0,\infty ),\gamma _\alpha )\) associated with the non-doubling probability measure \(d\gamma _\alpha (x)=\frac{2x^{2\alpha +1}}{\Gamma (\alpha +1)}e^{-x^2}dx\) on \((0,\infty )\), for \({\alpha >-\frac{1}{2}}\). We obtain characterizations of \(\mathcal {H}^1((0,\infty ),\gamma _\alpha )\) by using two local maximal functions. We also prove that the truncated maximal function defined through the heat semigroup generated by the Laguerre differential operator is bounded from \(\mathcal {H}^1((0,\infty ),\gamma _\alpha )\) into \(L^1((0,\infty ),\gamma _\alpha )\).

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
Collectanea Mathematica
Collectanea Mathematica 数学-数学
CiteScore
2.70
自引率
9.10%
发文量
36
审稿时长
>12 weeks
期刊介绍: Collectanea Mathematica publishes original research peer reviewed papers of high quality in all fields of pure and applied mathematics. It is an international journal of the University of Barcelona and the oldest mathematical journal in Spain. It was founded in 1948 by José M. Orts. Previously self-published by the Institut de Matemàtica (IMUB) of the Universitat de Barcelona, as of 2011 it is published by Springer.
×
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