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

  • Yongjiang DUAN ,
  • Sawlet JUNIS ,
  • Na ZHAN
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  • 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
Yongjiang DUAN, E-mail: duanyj086@nenu.edu.cn; Na ZHAN, E-mail: lxyzn@lnut.edu.cn

Received date: 2024-06-21

  Revised date: 2024-11-20

  Online published: 2025-10-10

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).

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.

Cite this article

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 . DOI: 10.1007/s10473-025-0414-1

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