Volterra operator acting on Bergman spaces of Dirichlet series

IF 1.7 2区 数学 Q1 MATHEMATICS
Carlos Gómez-Cabello , Pascal Lefèvre , Hervé Queffélec
{"title":"Volterra operator acting on Bergman spaces of Dirichlet series","authors":"Carlos Gómez-Cabello ,&nbsp;Pascal Lefèvre ,&nbsp;Hervé Queffélec","doi":"10.1016/j.jfa.2025.110906","DOIUrl":null,"url":null,"abstract":"<div><div>Since their introduction in 1997, Hardy spaces of Dirichlet series have been broadly studied. The increasing interest which they sparked motivated the introduction of new such spaces, as the Bergman spaces <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span> considered here, with <em>μ</em> a probability measure. Similarly, recent lines of research have focused on the study of some classical operators acting on these spaces, like the Volterra operator <span><math><msub><mrow><mi>V</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span>. In this work, we introduce a new family of spaces of Dirichlet series, the <span><math><msub><mrow><mtext>Bloch</mtext></mrow><mrow><mi>μ</mi></mrow></msub></math></span>-spaces. We can provide, in terms of those spaces, a sufficient condition for this Volterra operator to act boundedly on the spaces <span><math><msubsup><mrow><mi>A</mi></mrow><mrow><mi>μ</mi></mrow><mrow><mi>p</mi></mrow></msubsup></math></span>. We also establish a necessary condition for a specific choice of <em>μ</em>. Sufficient and necessary conditions for compactness are also proven. The non-membership in Schatten classes is established, as well as a radicality result for some Bloch space.</div></div>","PeriodicalId":15750,"journal":{"name":"Journal of Functional Analysis","volume":"289 3","pages":"Article 110906"},"PeriodicalIF":1.7000,"publicationDate":"2025-03-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Functional Analysis","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022123625000886","RegionNum":2,"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

Abstract

Since their introduction in 1997, Hardy spaces of Dirichlet series have been broadly studied. The increasing interest which they sparked motivated the introduction of new such spaces, as the Bergman spaces Aμp considered here, with μ a probability measure. Similarly, recent lines of research have focused on the study of some classical operators acting on these spaces, like the Volterra operator Vg. In this work, we introduce a new family of spaces of Dirichlet series, the Blochμ-spaces. We can provide, in terms of those spaces, a sufficient condition for this Volterra operator to act boundedly on the spaces Aμp. We also establish a necessary condition for a specific choice of μ. Sufficient and necessary conditions for compactness are also proven. The non-membership in Schatten classes is established, as well as a radicality result for some Bloch space.
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
3.20
自引率
5.90%
发文量
271
审稿时长
7.5 months
期刊介绍: The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis
×
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