从加权谐波布洛赫空间到加权谐波齐格蒙空间的合成算子规范

IF 1.9 3区 数学 Q1 MATHEMATICS Journal of Function Spaces Pub Date : 2024-03-16 DOI:10.1155/2024/5581805
Munirah Aljuaid, M. A. Bakhit
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We first give necessary and sufficient conditions where the composition operator between <svg height=\"16.0921pt\" style=\"vertical-align:-3.8339pt\" version=\"1.1\" viewbox=\"-0.0498162 -12.2582 20.7306 16.0921\" width=\"20.7306pt\" 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)\"><use xlink:href=\"#g198-3\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.35,-5.741)\"><use xlink:href=\"#g50-233\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.35,3.784)\"><use xlink:href=\"#g50-73\"></use></g></svg> and <svg height=\"17.5066pt\" style=\"vertical-align:-4.091pt\" version=\"1.1\" viewbox=\"-0.0498162 -13.4156 20.4958 17.5066\" width=\"20.4958pt\" 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)\"><use xlink:href=\"#g198-27\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.116,-6.899)\"><use xlink:href=\"#g50-224\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.116,4.041)\"><use xlink:href=\"#g50-73\"></use></g></svg> is bounded. Secondly, we will study the compactness case of the composition operator between <svg height=\"16.0921pt\" style=\"vertical-align:-3.8339pt\" version=\"1.1\" viewbox=\"-0.0498162 -12.2582 20.7306 16.0921\" width=\"20.7306pt\" 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)\"><use xlink:href=\"#g198-3\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.35,-5.741)\"><use xlink:href=\"#g50-233\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.35,3.784)\"><use xlink:href=\"#g50-73\"></use></g></svg> and <span><svg height=\"17.5066pt\" style=\"vertical-align:-4.091pt\" version=\"1.1\" viewbox=\"-0.0498162 -13.4156 20.4958 17.5066\" width=\"20.4958pt\" 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)\"><use xlink:href=\"#g198-27\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.116,-6.899)\"><use xlink:href=\"#g50-224\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.116,4.041)\"><use xlink:href=\"#g50-73\"></use></g></svg>.</span> Finally, we will estimate the essential norms of the composition operator between <svg height=\"16.0921pt\" style=\"vertical-align:-3.8339pt\" version=\"1.1\" viewbox=\"-0.0498162 -12.2582 20.7306 16.0921\" width=\"20.7306pt\" 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)\"><use xlink:href=\"#g198-3\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.35,-5.741)\"><use xlink:href=\"#g50-233\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.35,3.784)\"><use xlink:href=\"#g50-73\"></use></g></svg> and <span><svg height=\"17.5066pt\" style=\"vertical-align:-4.091pt\" version=\"1.1\" viewbox=\"-0.0498162 -13.4156 20.4958 17.5066\" width=\"20.4958pt\" 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)\"><use xlink:href=\"#g198-27\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.116,-6.899)\"><use xlink:href=\"#g50-224\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,12.116,4.041)\"><use xlink:href=\"#g50-73\"></use></g></svg>.</span>","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-03-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Norms of Composition Operators from Weighted Harmonic Bloch Spaces into Weighted Harmonic Zygmund Spaces\",\"authors\":\"Munirah Aljuaid, M. 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We first give necessary and sufficient conditions where the composition operator between <svg height=\\\"16.0921pt\\\" style=\\\"vertical-align:-3.8339pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -12.2582 20.7306 16.0921\\\" width=\\\"20.7306pt\\\" 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)\\\"><use xlink:href=\\\"#g198-3\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.35,-5.741)\\\"><use xlink:href=\\\"#g50-233\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.35,3.784)\\\"><use xlink:href=\\\"#g50-73\\\"></use></g></svg> and <svg height=\\\"17.5066pt\\\" style=\\\"vertical-align:-4.091pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -13.4156 20.4958 17.5066\\\" width=\\\"20.4958pt\\\" 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)\\\"><use xlink:href=\\\"#g198-27\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.116,-6.899)\\\"><use xlink:href=\\\"#g50-224\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.116,4.041)\\\"><use xlink:href=\\\"#g50-73\\\"></use></g></svg> is bounded. Secondly, we will study the compactness case of the composition operator between <svg height=\\\"16.0921pt\\\" style=\\\"vertical-align:-3.8339pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -12.2582 20.7306 16.0921\\\" width=\\\"20.7306pt\\\" 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)\\\"><use xlink:href=\\\"#g198-3\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.35,-5.741)\\\"><use xlink:href=\\\"#g50-233\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.35,3.784)\\\"><use xlink:href=\\\"#g50-73\\\"></use></g></svg> and <span><svg height=\\\"17.5066pt\\\" style=\\\"vertical-align:-4.091pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -13.4156 20.4958 17.5066\\\" width=\\\"20.4958pt\\\" 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)\\\"><use xlink:href=\\\"#g198-27\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.116,-6.899)\\\"><use xlink:href=\\\"#g50-224\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.116,4.041)\\\"><use xlink:href=\\\"#g50-73\\\"></use></g></svg>.</span> Finally, we will estimate the essential norms of the composition operator between <svg height=\\\"16.0921pt\\\" style=\\\"vertical-align:-3.8339pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -12.2582 20.7306 16.0921\\\" width=\\\"20.7306pt\\\" 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)\\\"><use xlink:href=\\\"#g198-3\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.35,-5.741)\\\"><use xlink:href=\\\"#g50-233\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.35,3.784)\\\"><use xlink:href=\\\"#g50-73\\\"></use></g></svg> and <span><svg height=\\\"17.5066pt\\\" style=\\\"vertical-align:-4.091pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -13.4156 20.4958 17.5066\\\" width=\\\"20.4958pt\\\" 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)\\\"><use xlink:href=\\\"#g198-27\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.116,-6.899)\\\"><use xlink:href=\\\"#g50-224\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,12.116,4.041)\\\"><use xlink:href=\\\"#g50-73\\\"></use></g></svg>.</span>\",\"PeriodicalId\":15840,\"journal\":{\"name\":\"Journal of Function Spaces\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-03-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Function Spaces\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1155/2024/5581805\",\"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 Function Spaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/5581805","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

本文研究了从加权谐波布洛赫空间到加权谐波齐格蒙空间的组成算子的规范。临界常数在开放的单位盘上。我们首先给出和之间的组成算子有界的必要条件和充分条件。其次，我们将研究 和 之间组成算子的紧凑性情况。最后，我们将估计 和 之间组成算子的基本规范。
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Norms of Composition Operators from Weighted Harmonic Bloch Spaces into Weighted Harmonic Zygmund Spaces
This article examines the norms of composition operators from the weighted harmonic Bloch space to the weighted harmonic Zygmund space . The critical norm is on the open unit disk. We first give necessary and sufficient conditions where the composition operator between and is bounded. Secondly, we will study the compactness case of the composition operator between and . Finally, we will estimate the essential norms of the composition operator between and .
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来源期刊
Journal of Function Spaces
Journal of Function Spaces MATHEMATICS, APPLIEDMATHEMATICS -MATHEMATICS
CiteScore
4.10
自引率
10.50%
发文量
451
审稿时长
15 weeks
期刊介绍： Journal of Function Spaces (formerly titled Journal of Function Spaces and Applications) publishes papers on all aspects of function spaces, functional analysis, and their employment across other mathematical disciplines. As well as original research, Journal of Function Spaces 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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