{"title":"遍历理论与分析中的振荡不等式:单参数与多参数观点","authors":"Mariusz Mirek, T. Szarek, James Wright","doi":"10.4171/rmi/1383","DOIUrl":null,"url":null,"abstract":". In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention to quantitative aspects of pointwise convergence phenomena from the point of view of oscillation estimates in both the single and several parameter settings. We establish a number of new oscillation inequalities and give new proofs for known results with elementary arguments.","PeriodicalId":49604,"journal":{"name":"Revista Matematica Iberoamericana","volume":" ","pages":""},"PeriodicalIF":1.3000,"publicationDate":"2022-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives\",\"authors\":\"Mariusz Mirek, T. Szarek, James Wright\",\"doi\":\"10.4171/rmi/1383\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention to quantitative aspects of pointwise convergence phenomena from the point of view of oscillation estimates in both the single and several parameter settings. We establish a number of new oscillation inequalities and give new proofs for known results with elementary arguments.\",\"PeriodicalId\":49604,\"journal\":{\"name\":\"Revista Matematica Iberoamericana\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":1.3000,\"publicationDate\":\"2022-09-03\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Revista Matematica Iberoamericana\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.4171/rmi/1383\",\"RegionNum\":2,\"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":"Revista Matematica Iberoamericana","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4171/rmi/1383","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
Oscillation inequalities in ergodic theory and analysis: one-parameter and multi-parameter perspectives
. In this survey we review useful tools that naturally arise in the study of pointwise convergence problems in analysis, ergodic theory and probability. We will pay special attention to quantitative aspects of pointwise convergence phenomena from the point of view of oscillation estimates in both the single and several parameter settings. We establish a number of new oscillation inequalities and give new proofs for known results with elementary arguments.
期刊介绍：
Revista Matemática Iberoamericana publishes original research articles on all areas of mathematics. Its distinguished Editorial Board selects papers according to the highest standards. Founded in 1985, Revista is a scientific journal of Real Sociedad Matemática Española.
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