{"title":"鞅极大算子的加权弱型不等式的统一形式","authors":"Yanbo B. Ren, Congbian Ma","doi":"10.1556/012.2021.58.2.1495","DOIUrl":null,"url":null,"abstract":"Let ɣ and Φ1 be nondecreasing and nonnegative functions defined on [0, ∞), and Φ2 is an N -function, u, v and w are weights. A unified version of weighted weak type inequality of the formfor martingale maximal operators f ∗ is considered, some necessary and su@cient conditions for it to hold are shown. In addition, we give a complete characterization of three-weight weak type maximal inequality of martingales. Our results generalize some known results on weighted theory of martingale maximal operators.","PeriodicalId":51187,"journal":{"name":"Studia Scientiarum Mathematicarum Hungarica","volume":"245 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"A Unified Version of Weighted Weak Type Inequality for Martingale Maximal Operators\",\"authors\":\"Yanbo B. Ren, Congbian Ma\",\"doi\":\"10.1556/012.2021.58.2.1495\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let ɣ and Φ1 be nondecreasing and nonnegative functions defined on [0, ∞), and Φ2 is an N -function, u, v and w are weights. A unified version of weighted weak type inequality of the formfor martingale maximal operators f ∗ is considered, some necessary and su@cient conditions for it to hold are shown. In addition, we give a complete characterization of three-weight weak type maximal inequality of martingales. Our results generalize some known results on weighted theory of martingale maximal operators.\",\"PeriodicalId\":51187,\"journal\":{\"name\":\"Studia Scientiarum Mathematicarum Hungarica\",\"volume\":\"245 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2021-06-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Studia Scientiarum Mathematicarum Hungarica\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1556/012.2021.58.2.1495\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studia Scientiarum Mathematicarum Hungarica","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1556/012.2021.58.2.1495","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
A Unified Version of Weighted Weak Type Inequality for Martingale Maximal Operators
Let ɣ and Φ1 be nondecreasing and nonnegative functions defined on [0, ∞), and Φ2 is an N -function, u, v and w are weights. A unified version of weighted weak type inequality of the formfor martingale maximal operators f ∗ is considered, some necessary and su@cient conditions for it to hold are shown. In addition, we give a complete characterization of three-weight weak type maximal inequality of martingales. Our results generalize some known results on weighted theory of martingale maximal operators.
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The journal publishes original research papers on various fields of mathematics, e.g., algebra, algebraic geometry, analysis, combinatorics, dynamical systems, geometry, mathematical logic, mathematical statistics, number theory, probability theory, set theory, statistical physics and topology.
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