具有倍权函数的Bergman空间上的Toeplitz和Hankel算子

中文摘要 AI 辅助

本文研究了在$\mathcal{D}$-加权Bergman空间$A_{\omega}^p$（$1\leq p<\infty$）上Toeplitz算子和Hankel算子的有界性与紧性。特别地，具有$\mathrm{BMO}_\omega^p$符号的Toeplitz算子在$A_{\omega}^p$上的有界性通过Berezin型变换进行了刻画。对于每个$1\leq p<\infty$，给出了具有局部可积符号的Toeplitz算子$T_f^\omega$有界（相应地，紧）的若干充分条件。此外，建立了具有共解析符号的Toeplitz算子$T_{\bar{f}}^\omega:A_\omega^1\rightarrow A_\omega^1$和Hankel算子$H_{\bar{f}}^\omega:A_\omega^1\rightarrow L_\omega^1$有界性的充分必要条件。

英文摘要

In this paper, we focus on the boundedness and compactness of the Toeplitz operators and the Hankel operators on the $\mathcal{D}$-weighted Bergman spaces $A_ω^p$ ($1\leq p<\infty$). In particular, the boundedness of Toeplitz operators with $\mathrm{BMO}_ω^p$-symbols on $A_ω^p$ is characterized in terms of the Berezin-type transform. Several sufficient conditions for the Toeplitz operators $T_f^ω$ with locally integrable symbols to be bounded (resp. compact) for each $1\leq p<\infty$ are presented. Moreover, sufficient and necessary conditions for the boundedness of the Toeplitz operator $T_{\bar{f}}^ω:A_ω^1\rightarrow A_ω^1$ and the Hankel operator $H_{\bar{f}}^ω:A_ω^1\rightarrow L_ω^1$ with co-analytic symbol are established.

发表机构

• Jinan University（暨南大学）
• Fudan University（复旦大学）
• Northeast Normal University（东北师范大学）
• Chongqing University（重庆大学）

机构由 AI 辅助整理，请以论文原文为准。