论文标题
Lipschitz型空间之间的乘法运算符在树上
Multiplication operators between Lipschitz-type spaces on a tree
论文作者
论文摘要
令$ \ MATHCAL {l} $为复杂值函数$ f $的空间，在植根于$ o $上的根源无限树的一组$ t $上，以使附近顶点的$ f $的值保持在整个树中的限制，并让$ \ net $ \ mathcal {l} $ { \ Mathcal {l} $使得$ | f（v）-f（v^ - ）| = o（| v |^{ - 1}）$，其中$ | v | $是$ o $和$ o $和$ v $和$ v $ and $ v^ - $是$ v $ v $ v $ of $ o $的邻居。在本文中，我们表征了$ \ Mathcal {l} $和$ \ Mathcal {l} _ {\ textbf {w}} $之间的有限和紧凑型运算符，并提供运算符标准和基本规范估计。此外，我们在$ \ mathcal {l} _ {\ textbf {w}} $和空格$ l^\ indy $ to $ t $ t $上的界限$ \ textbf {w}} $之间表征有界和紧凑的乘法运算符在$ t $上并确定其运营商的标准和基本规范。我们确定这些空间之间的乘法算子之间没有异构体。
Let $\mathcal{L}$ be the space of complex-valued functions $f$ on the set of vertices $T$ of an rooted infinite tree rooted at $o$ such that the difference of the values of $f$ at neighboring vertices remains bounded throughout the tree, and let $\mathcal{L}_{\textbf{w}}$ be the set of functions $f\in \mathcal{L}$ such that $|f(v)-f(v^-)|=O(|v|^{-1})$, where $|v|$ is the distance between $o$ and $v$ and $v^-$ is the neighbor of $v$ closest to $o$. In this article, we characterize the bounded and the compact multiplication operators between $\mathcal{L}$ and $\mathcal{L}_{\textbf{w}}$, and provide operator norm and essential norm estimates. Furthermore, we characterize the bounded and compact multiplication operators between $\mathcal{L}_{\textbf{w}}$ and the space $L^\infty$ of bounded functions on $T$ and determine their operator norm and their essential norm. We establish that there are no isometries among the multiplication operators between these spaces.
