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

Analysis and Geometry in Metric Spaces Pub Date : 2022-01-01 DOI:10.1515/agms-2022-0137

G. Lu, S. Tao, Miaomiao Wang

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.

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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。

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来源期刊

Analysis and Geometry in Metric Spaces Mathematics-Geometry and Topology

CiteScore

1.80

自引率

0.00%

发文量

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.