| 徐宁.Zygmund 空间到 Bloch 空间上径向导数算子与积分型算子的乘积[J].数学年刊A辑,2013,34(3):269~278 |
| Zygmund 空间到 Bloch 空间上径向导数算子与积分型算子的乘积 |
| Products of Radial Derivative Operator andIntegral-Type Operator from ZygmundSpaces to Bloch Spaces |
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| DOI： |
| 中文关键词: 径向导数算子, 积分型算子, Zygmund 空间, Bloch 空间 |
| 英文关键词:Radial derivative operator, Integral-type operator, Zygmund
space, Bloch space |
| 基金项目: |
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| 中文摘要: |
| 设$H(\mathbb{B})$为单位球上全纯函数类,研究了单位球上 Zygmund 空间到 Bloch 空间上径向导数算子$\Re$与积分型算子$I_\varphi^g$乘积的有界性和紧性,
这里
$$
I_\varphi^g f(z)=\int_0^1 \Re f(\varphi(tz))g(tz)\frac{{\rm d}t}{t},\quad z\in\mathbb{B},
$$
其中$g\in H(\mathbb{B}),\ g(0)=0$, $\varphi$ 是$\mathbb{B}$上全纯自映射. |
| 英文摘要: |
| Let $H(\mathbb{B})$ denote the space of all holomorphic functions on the unit ball
$\mathbb{B}\in \mathbb{C}^n$. The author investigates the boundedness and the compactness
of the product of the radial
derivative operator and the following integral-type operator:
$$
I_\varphi^g f(z)=\int_0^1 \Re f(\varphi(tz))g(tz)\frac{{\rm d}t}{t},\quad z\in\mathbb{B},
$$
from Zygmund spaces to
Bloch spaces, where $g\in H(\mathbb{B}),\ g(0)=0$, $\varphi$ is a holomorphic self-map of $\mathbb{B}$. |
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