{"title":"导数哈代空间上的组合-微分算子","authors":"A. Abkar, A. Babaei","doi":"10.1155/2024/8222237","DOIUrl":null,"url":null,"abstract":"We first explore conditions under which every weighted composition-differentiation operator on the Hardy space <svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 34.4579 13.8595\" width=\"34.4579pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,10.923,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,15.87,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,20.368,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,29.754,0)\"></path></g></svg> is completely continuous. We then discuss necessary and sufficient conditions for these operators to be Hilbert–Schmidt on the derivative Hardy space <span><svg height=\"13.8595pt\" style=\"vertical-align:-2.2681pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 29.656 13.8595\" width=\"29.656pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,6.136,-5.741)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,11.083,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,15.581,0)\"><use xlink:href=\"#g197-15\"></use></g><g transform=\"matrix(.013,0,0,-0.013,24.967,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>.</span>","PeriodicalId":54214,"journal":{"name":"Journal of Mathematics","volume":"4 1","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2024-01-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Composition-Differentiation Operators on Derivative Hardy Spaces\",\"authors\":\"A. Abkar, A. Babaei\",\"doi\":\"10.1155/2024/8222237\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We first explore conditions under which every weighted composition-differentiation operator on the Hardy space <svg height=\\\"13.8595pt\\\" style=\\\"vertical-align:-2.2681pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -11.5914 34.4579 13.8595\\\" width=\\\"34.4579pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,10.923,-5.741)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,15.87,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,20.368,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,29.754,0)\\\"></path></g></svg> is completely continuous. We then discuss necessary and sufficient conditions for these operators to be Hilbert–Schmidt on the derivative Hardy space <span><svg height=\\\"13.8595pt\\\" style=\\\"vertical-align:-2.2681pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -11.5914 29.656 13.8595\\\" width=\\\"29.656pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,6.136,-5.741)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,11.083,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,15.581,0)\\\"><use xlink:href=\\\"#g197-15\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,24.967,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg>.</span>\",\"PeriodicalId\":54214,\"journal\":{\"name\":\"Journal of Mathematics\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2024-01-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1155/2024/8222237\",\"RegionNum\":4,\"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 Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/8222237","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Composition-Differentiation Operators on Derivative Hardy Spaces
We first explore conditions under which every weighted composition-differentiation operator on the Hardy space is completely continuous. We then discuss necessary and sufficient conditions for these operators to be Hilbert–Schmidt on the derivative Hardy space .
期刊介绍：
Journal of Mathematics is a broad scope journal that publishes original research articles as well as review articles on all aspects of both pure and applied mathematics. As well as original research, Journal of Mathematics also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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