{"title":"解析希尔伯特空间上系数乘数的海尔-乌兰稳定性","authors":"Chun Wang, Tian-Zhou Xu","doi":"10.1007/s00009-024-02673-6","DOIUrl":null,"url":null,"abstract":"<p>In this paper, we investigate the Hyers–Ulam stability of the coefficient multipliers on the Hardy space <span>\\(H^2\\)</span> and the Bergman space <span>\\(A^2\\)</span>, meanwhile, we also investigate the Hyers–Ulam stability of the coefficient multipliers between the Bergman space <span>\\(A^2\\)</span> and the Hardy space <span>\\(H^2\\)</span>. We give the necessary and sufficient condition for the coefficient multipliers to have the Hyers–Ulam stability on the Hardy space <span>\\(H^2\\)</span>, on the Bergman space <span>\\(A^2\\)</span> and between the Bergman space <span>\\(A^2\\)</span> and the Hardy space <span>\\(H^2\\)</span>, respectively. We also show that the best constant of Hyers–Ulam stability exists under different circumstances. Some results generalized the results of MacGregor and Zhu when <span>\\(p=2\\)</span> in MacGregor and Zhu article (Mathematika 42:413–426, 1995). Moreover, some illustrative examples are also discussed.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Hyers–Ulam Stability of the Coefficient Multipliers on Analytic Hilbert Spaces\",\"authors\":\"Chun Wang, Tian-Zhou Xu\",\"doi\":\"10.1007/s00009-024-02673-6\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>In this paper, we investigate the Hyers–Ulam stability of the coefficient multipliers on the Hardy space <span>\\\\(H^2\\\\)</span> and the Bergman space <span>\\\\(A^2\\\\)</span>, meanwhile, we also investigate the Hyers–Ulam stability of the coefficient multipliers between the Bergman space <span>\\\\(A^2\\\\)</span> and the Hardy space <span>\\\\(H^2\\\\)</span>. We give the necessary and sufficient condition for the coefficient multipliers to have the Hyers–Ulam stability on the Hardy space <span>\\\\(H^2\\\\)</span>, on the Bergman space <span>\\\\(A^2\\\\)</span> and between the Bergman space <span>\\\\(A^2\\\\)</span> and the Hardy space <span>\\\\(H^2\\\\)</span>, respectively. We also show that the best constant of Hyers–Ulam stability exists under different circumstances. Some results generalized the results of MacGregor and Zhu when <span>\\\\(p=2\\\\)</span> in MacGregor and Zhu article (Mathematika 42:413–426, 1995). Moreover, some illustrative examples are also discussed.</p>\",\"PeriodicalId\":49829,\"journal\":{\"name\":\"Mediterranean Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-05-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mediterranean Journal of Mathematics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s00009-024-02673-6\",\"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":"Mediterranean Journal of Mathematics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s00009-024-02673-6","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Hyers–Ulam Stability of the Coefficient Multipliers on Analytic Hilbert Spaces
In this paper, we investigate the Hyers–Ulam stability of the coefficient multipliers on the Hardy space \(H^2\) and the Bergman space \(A^2\), meanwhile, we also investigate the Hyers–Ulam stability of the coefficient multipliers between the Bergman space \(A^2\) and the Hardy space \(H^2\). We give the necessary and sufficient condition for the coefficient multipliers to have the Hyers–Ulam stability on the Hardy space \(H^2\), on the Bergman space \(A^2\) and between the Bergman space \(A^2\) and the Hardy space \(H^2\), respectively. We also show that the best constant of Hyers–Ulam stability exists under different circumstances. Some results generalized the results of MacGregor and Zhu when \(p=2\) in MacGregor and Zhu article (Mathematika 42:413–426, 1995). Moreover, some illustrative examples are also discussed.
期刊介绍：
The Mediterranean Journal of Mathematics (MedJM) is a publication issued by the Department of Mathematics of the University of Bari. The new journal replaces the Conferenze del Seminario di Matematica dell’Università di Bari which has been in publication from 1954 until 2003.
The Mediterranean Journal of Mathematics aims to publish original and high-quality peer-reviewed papers containing significant results across all fields of mathematics. The submitted papers should be of medium length (not to exceed 20 printed pages), well-written and appealing to a broad mathematical audience.
In particular, the Mediterranean Journal of Mathematics intends to offer mathematicians from the Mediterranean countries a particular opportunity to circulate the results of their researches in a common journal. Through such a new cultural and scientific stimulus the journal aims to contribute to further integration amongst Mediterranean universities, though it is open to contribution from mathematicians across the world.
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