Wandering subspaces of the hardy-sobolev spaces over

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• 作者：Jiesheng XIAO ; ^{xiaojiesheng@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：wandering subspace ; invariant subspace ; Beurling's theorem ; Hardy-Sobolev space ; doubly commuting
• 刊名：Acta Mathematica Scientia
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：36
• 期：5
• 页码：1467-1473
• 全文大小：338 K

文摘

In this paper, we show that for$\frac{log\frac{2}{3}}{2log2}\le \beta \le \frac{1}{2}$, suppose S   is an invariant subspace of the Hardy-Sobolev spaces$H_{\beta }^2\left({\mathbb{D}}^n\right)$ for the n  -tuple of multiplication operators(M_z1,⋯,M_zn)$\left(M_{z_1},\cdots ,M_{z_n}\right)$. If(M_z1|_S,⋯,M_zn|_S)$\left(M_{z_1}{|}_S,\cdots ,M_{z_n}{|}_S\right)$ is doubly commuting, then for any non-empty sub-set α = {α₁, …,α_k} of {1, …, n  },$w_{\alpha }^S$ is a generating wandering subspace forM_α|_S=(M_zα1|_S,⋯,M_zαk|_S)$M_{\alpha }{|}_S=\left(M_{z_{{\alpha }_1}}{|}_S,\cdots ,M_{z_{{\alpha }_k}}{|}_S\right)$, that is,${\left[w_{\alpha }^S\right]}_{M_{\alpha }{|}_S}=S$, Where$w_{\alpha }^S=\underset{i=1}{\overset{k}{\cap }}\left(S\Theta z_{{\alpha }_i}S\right)$.