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

doi:10.1007/s10473-026-0216-0

Abstract

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).

Key words: logarithmic Forelli-Rudin type operator, weighted Lebesgue space, integral estimate, boundedness, unit ball

CLC Number:

47G10

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.

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