BOUNDEDNESS OF THE BERGMAN TYPE OPERATOR $T_{\lambda,\tau,c,k,k'}$ FROM $L^{p}(B_{n}, {\rm d}v_{\alpha})$ TO $L^{q}(B_{n}, {\rm d}v_{\beta})$

  • Xuejun ZHANG ,
  • Min ZHOU
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  • 1. College of Mathematics and Statistics, Hunan Normal University, Changsha 410081, China;
    2. School of Mathematics, Hunan University, Changsha 410082, China
Xuejun ZHANG, E-mail: xuejunttt@263.net

Received date: 2025-01-16

  Revised date: 2025-10-21

  Online published: 2026-05-22

Supported by

Zhang's work was supported by the Education Department Important Foundation of Hunan Province in China (23A0095).

Abstract

Bergman type operators are closely related to many basic problems on operator theory and function space theory. In this paper, we characterize the boundedness of logarithmic Bergman type operator $T_{\lambda,\tau,c,k,k'}$ from $L^{p}(B_{n}, {\rm d}v_{\alpha})$ to $L^{q}(B_{n}, {\rm d}v_{\beta})$ for some $1\leq p,q\leq+\infty$ and real $\alpha,\beta$. These results generalize the relevant work of some scholars. At the same time, we partially solve the problem, put forward by Chen et al. in JMAA (2024).

Cite this article

Xuejun ZHANG , Min ZHOU . BOUNDEDNESS OF THE BERGMAN TYPE OPERATOR $T_{\lambda,\tau,c,k,k'}$ FROM $L^{p}(B_{n}, {\rm d}v_{\alpha})$ TO $L^{q}(B_{n}, {\rm d}v_{\beta})$[J]. Acta mathematica scientia, Series B, 2026 , 46(2) : 812 -825 . DOI: 10.1007/s10473-026-0216-0

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