Cauchy-Szegö operator, quaternionic Siegel upper half space, commutator, weighted Morrey space

In the setting of quaternionic Heisenberg group $\mathscr H^{n-1}$, we characterize the boundedness and compactness of commutator $[b,\mathcal C]$ for the Cauchy--Szegö operator $\mathcal C$ on the weighted Morrey space $L_w^{p,\,κ}(\mathscr H^{n-1})$ with $p\in(1, \infty)$, $κ\in(0, 1)$ and $w\in A_p(\mathscr H^{n-1}).$ More precisely, we prove that $[b,\mathcal C]$ is bounded on $L_w^{p,\,κ}(\mathscr H^{n-1})$ if and only if $b\in {\rm BMO}(\mathscr H^{n-1})$. And $[b,\mathcal C]$ is compact on $L_w^{p,\,κ}(\mathscr H^{n-1})$ if and only if $b\in {\rm VMO}(\mathscr H^{n-1})$.

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