论文标题
同质树的耐边空间上的组成操作员
Composition operators on Hardy spaces of the homogenous rooted trees
论文作者
论文摘要
在\ cite {co-tp-lack}中，现有作者启动了组成运算符的研究，该研究对广义强大空间的离散类似物$ \ mathbb {t} _ {p} $定义在同质生根的树上。在本文中，我们给出了$ \ mathbb {t} _ {p} $和$ \ m athbb {t} _ {p，0} $ spaces并计算其操作员标准的组成运算符$ c_ϕ $的等效条件。我们还表征了可逆构图操作员以及$ \ Mathbb {t} _ {p} $和$ \ m athbb {t} _ {p，0} $ space上的等距组成运算符。另外，我们讨论了$ \ mathbb {t} _ {p} $上的$ c_ϕ $的紧凑性，最后证明了$ \ mathbb {t} _ {p，0} $ space上没有紧凑的构图操作员。
In \cite{CO-Tp-spaces}, the present authors initiated the study of composition operators on discrete analogue of generalized Hardy space $\mathbb{T}_{p}$ defined on a homogeneous rooted tree. In this article, we give equivalent conditions for the composition operator $C_ϕ$ to be bounded on $\mathbb{T}_{p}$ and on $\mathbb{T}_{p,0}$ spaces and compute their operator norm. We also characterize invertible composition operators as well as isometric composition operators on $\mathbb{T}_{p}$ and on $\mathbb{T}_{p,0}$ spaces. Also, we discuss the compactness of $C_ϕ$ on $\mathbb{T}_{p}$ and finally prove there are no compact composition operators on $\mathbb{T}_{p,0}$ spaces.
