Compactness for commutator of fractional integral on non-homogeneous Morrey spaces
Received:January 28, 2021  Revised:January 28, 2021
Key Word: Non-homogeneous metric measure space, compactness, commutator of the fractional integral, $\mathrm{Lip}_{\beta}(\mu)$, Morrey space
Fund ProjectL:Innovation Capacity Improvement Project for Colleges and Universities of Gansu Province
 Author Name Affiliation Address Guanghui Lu Northwest Normal University Anning West Road 967
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The aim of this paper is to establish the necessary and sufficient conditions of the compactness for the commutator of the fractional integral $[b, I_{\gamma}]$ generated by the fractional integral $I_{\gamma}$ and the function $b\in\mathrm{Lip}_{\beta}(\mu)$ on Morrey space over non-homogeneous metric measure space, which satisfies the upper doubling and geometrically doubling conditions in the sense of Hyt\"{o}nen. Under the assumption that the dominating function $\lambda$ satisfies the weak reverse doubling condition, the author proves that the commutator $[b,I_{\gamma}]$ is compact from the Morrey space $M^{p}_{q}(\mu)$ into the Morrey space $M^{s}_{t}(\mu)$ if and only if $b\in\mathrm{Lip}_{\beta}(\mu)$.