BERGMAN PROJECTION AND TOEPLITZ OPERATORS ON WEIGHTED HARMONIC BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS

doi:10.1007/s10473-025-0414-1

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (4): 1497-1513.doi: 10.1007/s10473-025-0414-1

BERGMAN PROJECTION AND TOEPLITZ OPERATORS ON WEIGHTED HARMONIC BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS

Yongjiang DUAN¹, Sawlet JUNIS^1,2,*, Na ZHAN³

1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;
2. School of Mathematics and Statistics, Yili Normal University, Yining 835000, China;
3. College of Science, Liaoning University of Technology, Jinzhou 121001, China

收稿日期:2024-06-21 修回日期:2024-11-20 出版日期:2025-10-10 发布日期:2025-10-10

BERGMAN PROJECTION AND TOEPLITZ OPERATORS ON WEIGHTED HARMONIC BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS

Yongjiang DUAN¹, Sawlet JUNIS^1,2,*, Na ZHAN³

1. School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;
2. School of Mathematics and Statistics, Yili Normal University, Yining 835000, China;
3. College of Science, Liaoning University of Technology, Jinzhou 121001, China

Received:2024-06-21 Revised:2024-11-20 Online:2025-10-10 Published:2025-10-10
Contact: ^*Sawlet JUNIS, E-mail: shawltjns@nenu.edu.cn
About author:Yongjiang DUAN, E-mail: duanyj086@nenu.edu.cn; Na ZHAN, E-mail: lxyzn@lnut.edu.cn
Supported by:
National Natural Science Foundation of China (12171075) and the Science and Technology Research Project of Education Department of Jilin Province (JJKH20241406KJ). Zhan's research was supported by the Doctoral Startup Fund of Liaoning University of Technology (XB2024029).

摘要/Abstract

摘要： In this paper, it is shown that the harmonic Bergman projection $P^h_{\omega}$, induced by a radial weight $\omega,$ is bounded and onto from $L^{\infty}(\mathbb{D})$ to the harmonic Bloch space $\mathcal{B}_{h}$ if and only if $\omega\in \mathcal{D}$, which is a class of radial weights satisfying the two-sided doubling conditions. As an application, the bounded and compact positive Toeplitz operators $T^h_{\mu,\omega}$ on the endpoint case weighted harmonic Bergman space $L^1_{h,\omega}(\mathbb{D})$ are characterized.

关键词: Bergman projection, Toeplitz operator, harmonic Bloch space, $\mathcal {D}$ weight

Abstract: In this paper, it is shown that the harmonic Bergman projection $P^h_{\omega}$, induced by a radial weight $\omega,$ is bounded and onto from $L^{\infty}(\mathbb{D})$ to the harmonic Bloch space $\mathcal{B}_{h}$ if and only if $\omega\in \mathcal{D}$, which is a class of radial weights satisfying the two-sided doubling conditions. As an application, the bounded and compact positive Toeplitz operators $T^h_{\mu,\omega}$ on the endpoint case weighted harmonic Bergman space $L^1_{h,\omega}(\mathbb{D})$ are characterized.

Key words: Bergman projection, Toeplitz operator, harmonic Bloch space, $\mathcal {D}$ weight

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.

Yongjiang DUAN, Sawlet JUNIS, Na ZHAN. BERGMAN PROJECTION AND TOEPLITZ OPERATORS ON WEIGHTED HARMONIC BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS[J]. Acta mathematica scientia,Series B, 2025, 45(4): 1497-1513.

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BERGMAN PROJECTION AND TOEPLITZ OPERATORS ON WEIGHTED HARMONIC BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS

BERGMAN PROJECTION AND TOEPLITZ OPERATORS ON WEIGHTED HARMONIC BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS

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