论文标题
类似于bloch型空间之间的类似cesàro的操作员
Cesàro-like operator acting between Bloch type spaces
论文作者
论文摘要
令$μ$为间隔$ [0,1）$和$ f（z）= \ sum_ {n = 0}^{\ infty} a_ {n} z^{n} \ in H（\ mathbb {d}）$的有限正borel度量。类似CeàSro的操作员由$$ \ MATHCAL {C}_μ（f）（z）= \ sum^\ infty_ {n = 0}μ_n\ left（\ sum^n_ {k = 0} a_k \ \ right） $μ_n$表示度量$μ$的$ n $ them-them-them_n = \ int _ {[0，1）} t^{n}dμ（t）$。在本文中，我们将$ \ Mathcal {c}_μ$的$μ$表征为$μ$，从一个bloch型空间界（紧凑），$ \ nathcal {b}^α$，将其变成另一个，$ \ nathcal {b}^β$。
Let $μ$ be a finite positive Borel measure on the interval $[0,1)$ and $f(z)=\sum_{n=0}^{\infty}a_{n}z^{n} \in H(\mathbb{D})$. The Ceàsro-like operator is defined by $$ \mathcal{C}_μ(f)(z)=\sum^\infty_{n=0}μ_n\left(\sum^n_{k=0}a_k\right)z^n, \ z\in \mathbb{D}, $$ where, for $n\geq 0$, $μ_n$ denotes the $n$-th moment of the measure $μ$, that is, $μ_n=\int_{[0, 1)} t^{n}dμ(t)$. In this paper, we characterize the measures $μ$ for which $\mathcal{C}_μ$ is bounded (compact) from one Bloch type space, $\mathcal {B}^α$, into another one, $\mathcal {B}^β$.
