{"title":"Iterated commutators under a joint condition on the tuple of multiplying functions","authors":"T. Hytonen, Kangwei Li, Tuomas Oikari","doi":"10.1090/proc/15101","DOIUrl":null,"url":null,"abstract":"We present a pair of joint conditions on the two functions $b_1,b_2$ strictly weaker than $b_1,b_2\\in \\operatorname{BMO}$ that almost characterize the $L^2$ boundedness of the iterated commutator $[b_2,[b_1,T]]$ of these functions and a Calder\\'on-Zygmund operator $T.$ Namely, we sandwich this boundedness between two bisublinear mean oscillation conditions of which one is a slightly bumped up version of the other.","PeriodicalId":8451,"journal":{"name":"arXiv: Classical Analysis and ODEs","volume":"12 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv: Classical Analysis and ODEs","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/proc/15101","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
We present a pair of joint conditions on the two functions $b_1,b_2$ strictly weaker than $b_1,b_2\in \operatorname{BMO}$ that almost characterize the $L^2$ boundedness of the iterated commutator $[b_2,[b_1,T]]$ of these functions and a Calder\'on-Zygmund operator $T.$ Namely, we sandwich this boundedness between two bisublinear mean oscillation conditions of which one is a slightly bumped up version of the other.