C. Bellavita , V. Daskalogiannis , G. Nikolaidis , G. Stylogiannis
{"title":"Optimal domain of generalized Volterra operators","authors":"C. Bellavita , V. Daskalogiannis , G. Nikolaidis , G. Stylogiannis","doi":"10.1016/j.jmaa.2024.128978","DOIUrl":null,"url":null,"abstract":"<div><div>For <em>g</em> in BMOA, we consider the generalized Volterra operator <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> acting on Hardy spaces <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>. This article aims to study the largest space of analytic functions, which is mapped by <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> into the Hardy space <span><math><msup><mrow><mi>H</mi></mrow><mrow><mi>p</mi></mrow></msup></math></span>. We call this space the optimal domain of <span><math><msub><mrow><mi>T</mi></mrow><mrow><mi>g</mi></mrow></msub></math></span> and we describe its structural properties. Motivation for this comes from the work of G. Curbera and W. Ricker <span><span>[7]</span></span> who studied the optimal domain of the classical Cesáro operator.</div></div>","PeriodicalId":50147,"journal":{"name":"Journal of Mathematical Analysis and Applications","volume":"543 2","pages":"Article 128978"},"PeriodicalIF":1.2000,"publicationDate":"2025-03-15","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/S0022247X24009004","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/10/22 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
For g in BMOA, we consider the generalized Volterra operator acting on Hardy spaces . This article aims to study the largest space of analytic functions, which is mapped by into the Hardy space . We call this space the optimal domain of and we describe its structural properties. Motivation for this comes from the work of G. Curbera and W. Ricker [7] who studied the optimal domain of the classical Cesáro operator.
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.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
