论文标题
Cauchy-Szegö操作员，Quaternionic Siegel上半部空间，换向器，加权莫雷空间
Cauchy-Szegö operator, quaternionic Siegel upper half space, commutator, weighted Morrey space
论文作者
论文摘要
在Quaternionic Heisenberg Group $ \ Mathscr H^{N-1} $的设置中，我们表征了Cauchy-szegöuterator$ $ $ \ \ \ \ \ \ \ \ n-1的cauchy-szegöuter$ $ $ \ n-1的界限带有$ p \ in（1，\ infty）$，$κ\ in（0，1）$和$ w \ in A_p（\ Mathscr H^{n-1}）。$更准确地说，我们证明$ [b，\ Mathcal c] $在$ l_w^{p，b，\ b，maths and $ b，nif if in $ l_w^nif if in $ b，nif}（ $ b \ in {\ rm bmo}（\ mathscr h^{n-1}）$。 $ [B，\ Mathcal C] $在$ l_w^{p，\，κ}（\ Mathscr H^{n-1}）$上是紧凑的，并且仅当$ b \ in {\ rm vmo}（\ rm vmo}（\ mathscr h^{n-1}}）中时，
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 $b\in {\rm VMO}(\mathscr H^{n-1})$.
