Multiplication operators, integration operators and companion operators on weighted Block space
Multiplication operators, integration operators and companion operators on weighted Block space
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DOI：
10.14492/hokmj/1285766201
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发表时间：
2005-02
影响因子：
0.5
通讯作者：
R. Yoneda
中科院分区：
文献类型：
--
作者：
R. Yoneda
令$g$ 为复平面$C$ 中开单位圆盘$D$ 上的解析函数。我们将研究布洛赫空间上的算子 \[\ I_{g}(h) (z) := \int_0^z h'( \zeta )g( \zeta) d \zeta \ , \ J_g(h) (z) := \int_0^z h( \zeta )g'( \zeta) d \zeta\] 。本文将研究$I_g$在$\alpha$-Bloch空间上的有界性和紧性，以及$I_g$和$J_g$在$\alpha$-Bloch空间上定义的乘积的有界性和紧性。这样我们就可以得到乘法运算符$M_g$与$\alpha$-Bloch空间上定义的运算符$I_g$、$J_g$的关系。
Let $g$ be an analytic function on the open unit disk $D$ in the complex plane $C$. We will study the following operator \[\ I_{g}(h) (z) := \int_0^z h'( \zeta )g( \zeta) d \zeta \ , \ J_g(h) (z) := \int_0^z h( \zeta )g'( \zeta) d \zeta\] on the Bloch space. In this paper, we will study the boundedness and compactness of $I_g$ on the $\alpha$-Bloch space , and the boundedness and compactness of products of $I_g$ and $J_g$ defined on the $\alpha$-Bloch space. And we will get the relationship of multiplication operator $M_g$ and the operators $I_g$, $J_g$ defined on the $\alpha$-Bloch space.