齐型空间上加权Morrey空间上的交换子

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.