GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF $\bf \mathbb{C}^{n}$

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF $\bf \mathbb{C}^{n}$

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF $\bf \mathbb{C}^{n}$

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF $\bf \mathbb{C}^{n}$

GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF $\bf \mathbb{C}^{n}$

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doi:10.1007/s10473-024-0407-5

数学物理学报(英文版) ›› 2024, Vol. 44 ›› Issue (4): 1301-1326.doi: 10.1007/s10473-024-0407-5

Xuejun ZHANG^1,*, Yuting GUO¹, Hongxin CHEN², Pengcheng TANG³

1. College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;
2. School of Mathematics, Hunan University, Changsha 410082, China;
3. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China

收稿日期:2023-01-04 修回日期:2023-10-14 出版日期:2024-08-25 发布日期:2024-08-30

Xuejun ZHANG^1,*, Yuting GUO¹, Hongxin CHEN², Pengcheng TANG³

1. College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;
2. School of Mathematics, Hunan University, Changsha 410082, China;
3. School of Mathematics and Computational Science, Hunan University of Science and Technology, Xiangtan 411201, China

Received:2023-01-04 Revised:2023-10-14 Online:2024-08-25 Published:2024-08-30
Contact: *E-mail: xuejunttt@263.net
About author:E-mail: 947016922@qq.com;1755310775@qq.com;www.tang-tpc.com@foxmail.com
Supported by:
Zhang's work was supported by the Natural Science Foundation of Hunan Province of China (2022JJ30369) and the Education Department Important Foundation of Hunan Province in China (23A0095).

摘要： In this paper, we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators $T_{\lambda,\tau,k}$ , $S_{\lambda,\tau,k}$ , $Q_{\lambda,\tau,k}$ and $R_{\lambda,\tau,k}$ are bounded between Lebesgue type spaces. In order to prove the main results, we first give some bidirectional estimates for several typical integrals.

关键词: Forelli-Rudin type operator, $L^{p,q,s,k}(B_{n})$ space, boundedness, unit ball

Abstract: In this paper, we investigate sufficient and necessary conditions such that generalized Forelli-Rudin type operators $T_{\lambda,\tau,k}$ , $S_{\lambda,\tau,k}$ , $Q_{\lambda,\tau,k}$ and $R_{\lambda,\tau,k}$ are bounded between Lebesgue type spaces. In order to prove the main results, we first give some bidirectional estimates for several typical integrals.

Key words: Forelli-Rudin type operator, $L^{p,q,s,k}(B_{n})$ space, boundedness, unit ball

中图分类号:

32A37

Xuejun ZHANG, Yuting GUO, Hongxin CHEN, Pengcheng TANG. GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF $\bf \mathbb{C}^{n}$ [J]. 数学物理学报(英文版), 2024, 44(4): 1301-1326.

Xuejun ZHANG, Yuting GUO, Hongxin CHEN, Pengcheng TANG. GENERALIZED FORELLI-RUDIN TYPE OPERATORS BETWEEN SEVERAL FUNCTION SPACES ON THE UNIT BALL OF $\bf \mathbb{C}^{n}$ [J]. Acta mathematica scientia,Series B, 2024, 44(4): 1301-1326.

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