齐型空间上加权Morrey空间上的交换子

IF 0.9 3区数学 Q2 MATHEMATICS

Analysis and Geometry in Metric Spaces Pub Date : 2020-01-01 DOI:10.1515/agms-2020-0116

Ruming Gong, Ji Li, Elodie Pozzi, Manasa N. Vempati

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引用次数: 9

摘要

摘要本文在Coifman和Weiss意义上研究齐次型（X，d，µ）空间上Calderón–Zygmund算子T的交换子的有界性和紧性。更确切地说，我们证明了交换子[b，T]在加权Morrey空间Lωp，k（X）L_\omega^{p，k}\left（X\right）上有界，其中κ∈（0，1）和ω∈Ap（X），1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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Commutators on Weighted Morrey Spaces on Spaces of Homogeneous Type

Abstract In this paper, we study the boundedness and compactness of the commutator of Calderón– Zygmund operators T on spaces of homogeneous type (X, d, µ) in the sense of Coifman and Weiss. More precisely, we show that the commutator [b, T] is bounded on the weighted Morrey space Lωp,k(X) L_\omega ^{p,k}\left( X \right) with κ ∈ (0, 1) and ω ∈ Ap(X), 1 < p < ∞, if and only if b is in the BMO space. We also prove that the commutator [b, T] is compact on the same weighted Morrey space if and only if b belongs to the VMO space. We note that there is no extra assumptions on the quasimetric d and the doubling measure µ.

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.