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arXiv · 2009.12694

A note on commutators on weighted Morrey spaces on spaces of homogeneous type

Ruming Gong·Ji Li·Elodie Pozzi·Manasa N. Vempati
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Abstract

In this paper we study the boundedness and compactness characterizations 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 weighted Morrey space $L_ω^{p,κ}(X)$ ($κ\in(0,1), ω\in A_{p}(X), 1<p<\infty$) if and only if $b$ is in the BMO space. Moreover, the commutator $[b, T]$ is compact on weighted Morrey space $L_ω^{p,κ}(X)$ ($κ\in(0,1), ω\in A_{p}(X), 1<p<\infty$) if and only if $b$ is in the VMO space.

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Ruming Gong, Ji Li, Elodie Pozzi, Manasa N. Vempati. 2020-09-29. A note on commutators on weighted Morrey spaces on spaces of homogeneous type. https://arxiv.org/abs/2009.12694

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