多圆盘上Bergman空间和Dirichlet空间的游荡子空间
Wandering subspaces of the Bergman space and the Dirichlet space over polydisc
摘要：
研究了单位多圆盘$\mathbb{D}^n$（含$ n \geq 2$）上Bergman空间和Dirichlet空间的不变子空间的双交换性.证明了对$\{1,\dots,n\}$的任意非空子集$α=\{α_1,\dots,α_k\}$和$\D^n$上Bergman空间或Dirichlet空间的双交换不变子空间$\s$，由坐标乘法算子限制构成的元组$M_α|_\s:=(M_{z_{α_1}}|_\s,\dots, M_{z_{α_k}}|_\s)$总是具有形式为\[\bigcap_{i=1}^k(\s\ominus z_{α_i}\s). \]的游荡子空间
英文摘要：
Doubly commutativity of invariant subspaces of the Bergman space and the Dirichlet space over the unit polydisc $\mathbb{D}^n$ (with $ n \geq 2$) is investigated. We show that for any non-empty subset $α=\{α_1,\dots,α_k\}$ of $\{1,\dots,n\}$ and doubly commuting invariant subspace $\s$ of the Bergman space or the Dirichlet space over $\D^n$, the tuple consists of restrictions of co-ordinate multiplication operators $M_α|_\s:=(M_{z_{α_1}}|_\s,\dots, M_{z_{α_k}}|_\s)$ always possesses wandering subspace of the form \[\bigcap_{i=1}^k(\s\ominus z_{α_i}\s). \]
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