论文标题
带有本地集成符号的单位球上的托管操作员
Toeplitz operators on the unit ball with locally integrable symbols
论文作者
论文摘要
我们研究了Toeplitz运算符$t_ψ$的界限，并在$ \ mathbb {r}^n $的单位球上加权谐波伯格曼空间上的本地集成符号。在分析功能空间中概括了早期的结果，我们在合适的符号平均值方面得出了$t_ψ$的界限的一般条件。我们还获得了类似的“消失”条件，以实现紧凑性。最后，我们展示了如何将这些结果传输到分析功能的标准加权伯格曼空间的设置。
We study the boundedness of Toeplitz operators $T_ψ$ with locally integrable symbols on weighted harmonic Bergman spaces over the unit ball of $\mathbb{R}^n$. Generalizing earlier results for analytic function spaces, we derive a general sufficient condition for the boundedness of $T_ψ$ in terms of suitable averages of its symbol. We also obtain a similar "vanishing" condition for compactness. Finally, we show how these results can be transferred to the setting of the standard weighted Bergman spaces of analytic functions.
