{"title":"大Herz-Morrey空间上Marcinkiewicz积分算子高阶对易子的BMO估计","authors":"Babar SULTAN, Mehvish SULTAN, Ferit GÜRBÜZ","doi":"10.31801/cfsuasmas.1328691","DOIUrl":null,"url":null,"abstract":"Let $\\mathbb{S}^{n-1}$ denote the unit sphere in $\\mathbb{R}^n$ with the normalized Lebesgue measure. Let $\\Phi\\in L^{r}(\\mathbb{S}^{n-1})$ is a homogeneous function of degree zero and $b$ is a locally integrable function on $\\mathbb{R}^n$. In this paper we define the higher order commutators of Marcinkiewicz integral $[b,\\mu_{\\Phi}]^m$ and prove the boundedness of $[b,\\mu_{\\Phi}]^m$ under some proper assumptions on grand variable Herz-Morrey spaces $M\\dot{K}^{\\alpha(.),\\beta}_{u,v(.)}(\\mathbb{R}^n)$.","PeriodicalId":44692,"journal":{"name":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","volume":"47 1","pages":"0"},"PeriodicalIF":0.7000,"publicationDate":"2023-08-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"BMO estimate for the higher order commutators of Marcinkiewicz integral operator on grand Herz-Morrey spaces\",\"authors\":\"Babar SULTAN, Mehvish SULTAN, Ferit GÜRBÜZ\",\"doi\":\"10.31801/cfsuasmas.1328691\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let $\\\\mathbb{S}^{n-1}$ denote the unit sphere in $\\\\mathbb{R}^n$ with the normalized Lebesgue measure. Let $\\\\Phi\\\\in L^{r}(\\\\mathbb{S}^{n-1})$ is a homogeneous function of degree zero and $b$ is a locally integrable function on $\\\\mathbb{R}^n$. In this paper we define the higher order commutators of Marcinkiewicz integral $[b,\\\\mu_{\\\\Phi}]^m$ and prove the boundedness of $[b,\\\\mu_{\\\\Phi}]^m$ under some proper assumptions on grand variable Herz-Morrey spaces $M\\\\dot{K}^{\\\\alpha(.),\\\\beta}_{u,v(.)}(\\\\mathbb{R}^n)$.\",\"PeriodicalId\":44692,\"journal\":{\"name\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"volume\":\"47 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-08-21\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.31801/cfsuasmas.1328691\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications Faculty of Sciences University of Ankara-Series A1 Mathematics and Statistics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.31801/cfsuasmas.1328691","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
BMO estimate for the higher order commutators of Marcinkiewicz integral operator on grand Herz-Morrey spaces
Let $\mathbb{S}^{n-1}$ denote the unit sphere in $\mathbb{R}^n$ with the normalized Lebesgue measure. Let $\Phi\in L^{r}(\mathbb{S}^{n-1})$ is a homogeneous function of degree zero and $b$ is a locally integrable function on $\mathbb{R}^n$. In this paper we define the higher order commutators of Marcinkiewicz integral $[b,\mu_{\Phi}]^m$ and prove the boundedness of $[b,\mu_{\Phi}]^m$ under some proper assumptions on grand variable Herz-Morrey spaces $M\dot{K}^{\alpha(.),\beta}_{u,v(.)}(\mathbb{R}^n)$.