• •

### Volterra算子与Toeplitz算子的乘积

1. 1重庆工商大学数学与统计学院 重庆 400067
2经济社会应用统计重庆市重点实验室 重庆 400067
• 收稿日期:2023-05-25 修回日期:2023-10-12 出版日期:2024-08-26 发布日期:2024-07-26
• 通讯作者: *李永宁, E-mail:yongningli@ctbu.edu.cn
• 作者简介:丁宣浩, E-mail:dingxuanhao@ctbu.edu.cn;|邵长慧, E-mail: schdliyx@163.com
• 基金资助:
国家自然科学基金(12101092);重庆市自然科学基金(CSTB2022NSCQ-MSX1045);重庆市教委科学技术研究项目(KJQN202100822)

### The Product of Volterra Operator and Toeplitz Operator

Ding Xuanhao1,2(),Shao Changhui1(),Li Yongning1,2,*()

1. 1School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067
2Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing 400067
• Received:2023-05-25 Revised:2023-10-12 Online:2024-08-26 Published:2024-07-26
• Supported by:
National Natural Science Foundation of China(12101092);Chongqing Natural Science Foundation(CSTB2022NSCQ-MSX1045);Science and Technology Research Program of Chongqing Municipal Education Commission(KJQN202100822)

Abstract:

In this paper, we study the product operators of Volterra operator $V$ and Toeplitz operator $T_\varphi$ on the classical Hardy space $L_\varphi=T_\varphi V$ and $R_\varphi=VT_\varphi$, and we obtain some basic properties of $L_\varphi$ and $R_\varphi$, we also get a result of $L_\varphi$ which is similar to the Coburn theorem of Toeplitz operator. The necessary and sufficient conditions for $V$ and $T_\varphi$ to be commutative are given in this paper, and the symbol of $L_\varphi$ and $R_\varphi$ is characterized when $z^jH^2\ (j=1, 2, \cdots )$ are the common invariant subspaces of $L_\varphi$ and $R_\varphi$.

• O177.1