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

Abstract

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

arXiv admin note: text overlap with arXiv:1908.03040; substantial text overlap with arXiv:1908.08626 by other authors

Cited by in corpus (1)

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