Fractional Type Marcinkiewicz Integral Operator Associated with Θ-Type Generalized Fractional Kernel and Its Commutator on Non-homogeneous Spaces

IF 0.9 3区 数学 Q2 MATHEMATICS
G. Lu, S. Tao, Miaomiao Wang
{"title":"Fractional Type Marcinkiewicz Integral Operator Associated with Θ-Type Generalized Fractional Kernel and Its Commutator on Non-homogeneous Spaces","authors":"G. Lu, S. Tao, Miaomiao Wang","doi":"10.1515/agms-2022-0137","DOIUrl":null,"url":null,"abstract":"Abstract Let (𝒳, d, μ) be a non-homogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. Under assumption that θ and dominating function λ satisfy certain conditions, the authors prove that fractional type Marcinkiewicz integral operator M˜ \\tilde M α,lρ,q associated with θ-type generalized fractional kernel is bounded from the generalized Morrey space ℒr,ϕp/r,κ (μ) into space ℒp,ϕ,κ (μ), and bounded from the Lebesgue space Lr(μ) into space Lp(μ). Furthermore, the boundedness of commutator M˜ \\tilde M α,l,ρq,b generated by b∈RBMO˜(μ) b \\in \\widetilde {RBMO}\\left( \\mu \\right) and the M˜ \\tilde M α,l,ρq,b on space ℒp(μ) and on space ℒp,ϕ,κ (μ) is also obtained.","PeriodicalId":48637,"journal":{"name":"Analysis and Geometry in Metric Spaces","volume":null,"pages":null},"PeriodicalIF":0.9000,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Geometry in Metric Spaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1515/agms-2022-0137","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 1

Abstract

Abstract Let (𝒳, d, μ) be a non-homogeneous metric measure space satisfying the upper doubling and geometrically doubling conditions in the sense of Hytönen. Under assumption that θ and dominating function λ satisfy certain conditions, the authors prove that fractional type Marcinkiewicz integral operator M˜ \tilde M α,lρ,q associated with θ-type generalized fractional kernel is bounded from the generalized Morrey space ℒr,ϕp/r,κ (μ) into space ℒp,ϕ,κ (μ), and bounded from the Lebesgue space Lr(μ) into space Lp(μ). Furthermore, the boundedness of commutator M˜ \tilde M α,l,ρq,b generated by b∈RBMO˜(μ) b \in \widetilde {RBMO}\left( \mu \right) and the M˜ \tilde M α,l,ρq,b on space ℒp(μ) and on space ℒp,ϕ,κ (μ) is also obtained.
与Θ-Type广义分数核相关的分数型Marcinkiewicz积分算子及其在非齐次空间上的交换子
设(f, d, μ)是满足Hytönen意义上的上加倍和几何加倍条件的非齐次度量度量空间。在θ和主导函数λ满足一定条件的假设下,证明了与θ型广义分数型核相关的分数型Marcinkiewicz积分算子M ~ \tilde M α,lρ,q从广义Morrey空间∑,ϕ /r,κ (μ)有界到∑,φ,κ (μ)空间,并从Lebesgue空间Lr(μ)有界到∑(μ)空间。此外,还得到了由b∈RBMO≈(μ) b \in\widetilde RBMO \left ({}\mu\right)生成的换向子M ~ \tilde M α,l,ρq,b和M ~ \tilde M α,l,ρq,b在空间__p (μ)和空间__p, φ,κ (μ)上的有界性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
Analysis and Geometry in Metric Spaces
Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology
CiteScore
1.80
自引率
0.00%
发文量
8
审稿时长
16 weeks
期刊介绍: Analysis and Geometry in Metric Spaces is an open access electronic journal that publishes cutting-edge research on analytical and geometrical problems in metric spaces and applications. We strive to present a forum where all aspects of these problems can be discussed. AGMS is devoted to the publication of results on these and related topics: Geometric inequalities in metric spaces, Geometric measure theory and variational problems in metric spaces, Analytic and geometric problems in metric measure spaces, probability spaces, and manifolds with density, Analytic and geometric problems in sub-riemannian manifolds, Carnot groups, and pseudo-hermitian manifolds. Geometric control theory, Curvature in metric and length spaces, Geometric group theory, Harmonic Analysis. Potential theory, Mass transportation problems, Quasiconformal and quasiregular mappings. Quasiconformal geometry, PDEs associated to analytic and geometric problems in metric spaces.
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信