PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

doi:10.1007/s10473-024-0408-4

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (4): 1327-1336.doi: 10.1007/s10473-024-0408-4

PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

Zuoling Liu, Hasi Wulan^*

Department of Mathematics, Shantou University, Shantou 515063, China

收稿日期:2023-03-06 出版日期:2024-08-25 发布日期:2024-08-30

PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

Zuoling Liu, Hasi Wulan^*

Department of Mathematics, Shantou University, Shantou 515063, China

Received:2023-03-06 Online:2024-08-25 Published:2024-08-30
Contact: *E-mail: 16zlliu1@stu.edu.cn; zlliustu@163.com
About author:E-mail: 16zlliu1@stu.edu.cn; zlliustu@163.com
Supported by:
The work was supported by the NSFC (11720101003, 12071272).

摘要/Abstract

摘要： For analytic functions $u,\psi$ in the unit disk $\mathbb{D}$ in the complex plane and an analytic self-map $\varphi$ of $\mathbb{D}$, we describe in this paper the boundedness and compactness of product type operators$T_{u,\psi,\varphi}f(z)=u(z)f(\varphi(z))+\psi(z)f'(\varphi(z)), \quad z\in\mathbb{D},$ acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

关键词: compactness, boundedness, Bloch type space, product type operator, weighted Bergman space

Abstract: For analytic functions $u,\psi$ in the unit disk $\mathbb{D}$ in the complex plane and an analytic self-map $\varphi$ of $\mathbb{D}$, we describe in this paper the boundedness and compactness of product type operators$T_{u,\psi,\varphi}f(z)=u(z)f(\varphi(z))+\psi(z)f'(\varphi(z)), \quad z\in\mathbb{D},$ acting between weighted Bergman spaces induced by a doubling weight and a Bloch type space with a radial weight.

Key words: compactness, boundedness, Bloch type space, product type operator, weighted Bergman space

中图分类号:

47B33

Zuoling Liu, Hasi Wulan. PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES[J]. 数学物理学报(英文版), 2024, 44(4): 1327-1336.

Zuoling Liu, Hasi Wulan. PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES[J]. Acta mathematica scientia,Series B, 2024, 44(4): 1327-1336.

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PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

PRODUCT TYPE OPERATORS ACTING BETWEEN WEIGHTED BERGMAN SPACES AND BLOCH TYPE SPACES

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