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BY 4.0 license Open Access Published by De Gruyter Open Access December 21, 2020

Commutators on Weighted Morrey Spaces on Spaces of Homogeneous Type

  • Ruming Gong , Ji Li EMAIL logo , Elodie Pozzi and Manasa N. Vempati

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) 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.

MSC 2010: 42B20; 43A80

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Received: 2020-07-21
Accepted: 2020-11-09
Published Online: 2020-12-21

© 2020 Ruming Gong et al., published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 International License.

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