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

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

Xuejun ZHANG1,*, Yuting GUO1, Hongxin CHEN2, Pengcheng TANG3   

  1. 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

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

Xuejun ZHANG1,*, Yuting GUO1, Hongxin CHEN2, Pengcheng TANG3   

  1. 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