{"title":"Boundedness Characterization of Maximal Commutators on Orlicz Spaces in the Dunkl Setting","authors":"Vagif S. Guliyev sci","doi":"10.4208/jms.v53n1.20.03","DOIUrl":null,"url":null,"abstract":"On the real line, the Dunkl operators Dν( f )(x) := d f (x) dx +(2ν+1) f (x)− f (−x) 2x , ∀x∈R, ∀ν≥− 1 2 are differential-difference operators associated with the reflection group Z2 on R, and on the Rd the Dunkl operators { Dk,j }d j=1 are the differential-difference operators associated with the reflection group Zd 2 on R d. In this paper, in the setting R we show that b ∈ BMO(R,dmν) if and only if the maximal commutator Mb,ν is bounded on Orlicz spaces LΦ(R,dmν). Also in the setting Rd we show that b∈ BMO(R,hk(x)dx) if and only if the maximal commutator Mb,k is bounded on Orlicz spaces LΦ(R,hk(x)dx). AMS subject classifications: 42B20, 42B25, 42B35","PeriodicalId":43526,"journal":{"name":"数学研究","volume":" ","pages":""},"PeriodicalIF":0.8000,"publicationDate":"2020-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"数学研究","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.4208/jms.v53n1.20.03","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 2
Abstract
On the real line, the Dunkl operators Dν( f )(x) := d f (x) dx +(2ν+1) f (x)− f (−x) 2x , ∀x∈R, ∀ν≥− 1 2 are differential-difference operators associated with the reflection group Z2 on R, and on the Rd the Dunkl operators { Dk,j }d j=1 are the differential-difference operators associated with the reflection group Zd 2 on R d. In this paper, in the setting R we show that b ∈ BMO(R,dmν) if and only if the maximal commutator Mb,ν is bounded on Orlicz spaces LΦ(R,dmν). Also in the setting Rd we show that b∈ BMO(R,hk(x)dx) if and only if the maximal commutator Mb,k is bounded on Orlicz spaces LΦ(R,hk(x)dx). AMS subject classifications: 42B20, 42B25, 42B35
期刊介绍:
Journal of Mathematical Study (JMS) is a comprehensive mathematical journal published jointly by Global Science Press and Xiamen University. It publishes original research and survey papers, in English, of high scientific value in all major fields of mathematics, including pure mathematics, applied mathematics, operational research, and computational mathematics.