{"title":"康托洛维奇算子在变指数勒贝格空间中的近似率的直接估计值","authors":"Borislav R. Draganov, Ivan Gadjev","doi":"10.1007/s00009-024-02650-z","DOIUrl":null,"url":null,"abstract":"<p>We establish two direct estimates by <i>K</i>-functionals of the rate of approximation by the Kantorovich operators in variable exponent Lebesgue spaces. They extend known results in the non-variable exponent Lebesgue spaces. The approach applied heavily relies on the boundedness of the Hardy–Littlewood maximal operator.</p>","PeriodicalId":49829,"journal":{"name":"Mediterranean Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2024-05-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Direct Estimates of the Rate of Approximation by the Kantorovich Operator in Variable Exponent Lebesgue Spaces\",\"authors\":\"Borislav R. Draganov, Ivan Gadjev\",\"doi\":\"10.1007/s00009-024-02650-z\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We establish two direct estimates by <i>K</i>-functionals of the rate of approximation by the Kantorovich operators in variable exponent Lebesgue spaces. They extend known results in the non-variable exponent Lebesgue spaces. The approach applied heavily relies on the boundedness of the Hardy–Littlewood maximal operator.</p>\",\"PeriodicalId\":49829,\"journal\":{\"name\":\"Mediterranean Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-05-04\",\"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/s00009-024-02650-z\",\"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/s00009-024-02650-z","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
我们通过 K 函数对可变指数 Lebesgue 空间中 Kantorovich 算子的逼近率建立了两个直接估计。它们扩展了非可变指数勒贝格空间的已知结果。所应用的方法在很大程度上依赖于哈代-利特尔伍德最大算子的有界性。
Direct Estimates of the Rate of Approximation by the Kantorovich Operator in Variable Exponent Lebesgue Spaces
We establish two direct estimates by K-functionals of the rate of approximation by the Kantorovich operators in variable exponent Lebesgue spaces. They extend known results in the non-variable exponent Lebesgue spaces. The approach applied heavily relies on the boundedness of the Hardy–Littlewood maximal operator.
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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