大Herz-Morrey空间上Marcinkiewicz积分算子高阶对易子的BMO估计

Babar SULTAN, Mehvish SULTAN, Ferit GÜRBÜZ
{"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":null,"pages":null},"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\":null,\"pages\":null},\"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}
引用次数: 0

摘要

设$\mathbb{S}^{n-1}$用归一化勒贝格测度表示$\mathbb{R}^n$中的单位球。设$\Phi\in L^{r}(\mathbb{S}^{n-1})$是零次齐次函数,$b$是$\mathbb{R}^n$上的一个局部可积函数。本文定义了Marcinkiewicz积分$[b,\mu_{\Phi}]^m$的高阶对易子,并在大变量Herz-Morrey空间$M\dot{K}^{\alpha(.),\beta}_{u,v(.)}(\mathbb{R}^n)$上证明了$[b,\mu_{\Phi}]^m$的有界性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
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 $M\dot{K}^{\alpha(.),\beta}_{u,v(.)}(\mathbb{R}^n)$.
求助全文
通过发布文献求助,成功后即可免费获取论文全文。 去求助
来源期刊
自引率
0.00%
发文量
61
期刊最新文献
BMO estimate for the higher order commutators of Marcinkiewicz integral operator on grand Herz-Morrey spaces The type I heavy-tailed odd power generalized Weibull-G family of distributions with applications A Diophantine equation including Fibonacci and Fibonomial coefficients Quasi hemi-slant pseudo-Riemannian submersions in para-complex geometry On the curves lying on parallel-like surfaces of the ruled surface in $E^{3}$
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1