BOUNDEDNESS OF FORELLI-RUDIN TYPE OPERATORS ON TUBE DOMAINS OVER THE FORWARD LIGHT CONES

doi:10.1007/s10473-025-0401-6

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (4): 1235-1246.doi: 10.1007/s10473-025-0401-6

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BOUNDEDNESS OF FORELLI-RUDIN TYPE OPERATORS ON TUBE DOMAINS OVER THE FORWARD LIGHT CONES

Jiaxin LIU¹, Guantie DENG², Zhiqiang GAO²

1. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai 519082, China;
2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

收稿日期:2024-01-16 修回日期:2024-04-22 出版日期:2025-10-10 发布日期:2025-10-10

BOUNDEDNESS OF FORELLI-RUDIN TYPE OPERATORS ON TUBE DOMAINS OVER THE FORWARD LIGHT CONES

Jiaxin LIU¹, Guantie DENG², Zhiqiang GAO²

1. School of Mathematics (Zhuhai), Sun Yat-sen University, Zhuhai 519082, China;
2. School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received:2024-01-16 Revised:2024-04-22 Online:2025-10-10 Published:2025-10-10
Contact: ^*Guantie DENG, E-mail: denggt@bnu:edu:cn
About author:Jiaxin LIU, E-mail: liujx273@mail sysueducn; Zhiqiang GAO, E-mail: gaozq@bnueducn
Supported by:
Fundamental Research Funds for the Central Universities, Sun Yat-sen University (31610030). Deng's research was supported by the NSFC (11971042, 12071035) and the National Key R&D Program of China (2021YFA1002600).

摘要/Abstract

摘要： We explore some necessary and sufficient conditions for the boundedness of the Forelli-Rudin type operator $T$ on the weighted Lebesgue space associated with tubular domains over the forward light cone. Our approach involves conducting precise computations for a series of complex integrals to identify appropriate test functions, and through a detailed analysis of these test functions, we derive the boundedness properties of the operator $T$. This work is significant in the study of the Bergman projection operators.

关键词: Forelli-Rudin type operators, test function, light cone, Bergman projection

Abstract: We explore some necessary and sufficient conditions for the boundedness of the Forelli-Rudin type operator $T$ on the weighted Lebesgue space associated with tubular domains over the forward light cone. Our approach involves conducting precise computations for a series of complex integrals to identify appropriate test functions, and through a detailed analysis of these test functions, we derive the boundedness properties of the operator $T$. This work is significant in the study of the Bergman projection operators.

Key words: Forelli-Rudin type operators, test function, light cone, Bergman projection

Jiaxin LIU, Guantie DENG, Zhiqiang GAO. BOUNDEDNESS OF FORELLI-RUDIN TYPE OPERATORS ON TUBE DOMAINS OVER THE FORWARD LIGHT CONES[J]. 数学物理学报(英文版), 2025, 45(4): 1235-1246.

Jiaxin LIU, Guantie DENG, Zhiqiang GAO. BOUNDEDNESS OF FORELLI-RUDIN TYPE OPERATORS ON TUBE DOMAINS OVER THE FORWARD LIGHT CONES[J]. Acta mathematica scientia,Series B, 2025, 45(4): 1235-1246.

[1]	Yongjiang DUAN, Sawlet JUNIS, Na ZHAN. BERGMAN PROJECTION AND TOEPLITZ OPERATORS ON WEIGHTED HARMONIC BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS[J]. 数学物理学报(英文版), 2025, 45(4): 1497-1513.
[2]	周立芳, 樊云, 卢金. THE PRECISE NORM OF A CLASS OF FORELLI-RUDIN TYPE OPERATORS ON THE SIEGEL UPPER HALF SPACE[J]. 数学物理学报(英文版), 2021, 41(5): 1537-1546.

BOUNDEDNESS OF FORELLI-RUDIN TYPE OPERATORS ON TUBE DOMAINS OVER THE FORWARD LIGHT CONES

BOUNDEDNESS OF FORELLI-RUDIN TYPE OPERATORS ON TUBE DOMAINS OVER THE FORWARD LIGHT CONES

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