标题： 绝对求和的Toeplitz算子在Fock空间上 显示英文标题

标题： Absolutely Summing Toeplitz operators on Fock spaces

摘要： 对于$1\le p<\infty$，令$F^p_\varphi$是在${\mathbb C}^n$上的 Fock 空间，其权函数为$\varphi$，使得\(\varphi \in {\mathcal{C}}^{2}\left( {\mathbb{C}}^{n}\right)\)为实值且满足 $ m{\omega }_{0} \leq d{d}^{c}\varphi \leq M{\omega }_{0} $ 对于两个正常数\(m\)和\(M\)，\({\omega }_{0} = d{d}^{c}{\left| z\right| }^{2}\)是在\({\mathbb{C}}^{n}\)上的欧几里得 Kähler 形式， \({d}^{c} = \frac{\sqrt{-1}}{4}\left( {\bar{\partial } - \partial }\right)\)。 在本文中，我们完全表征了那些正Borel测度$\mu$在${\mathbb C}^n$上，使得由其诱导的Toeplitz算子$T_\mu$在$F_{\varphi}^{p}$上是$r$-求和的，对于$r \ge 1$。 显示英文摘要

摘要： For $1\le p<\infty$, let $F^p_\varphi$ be the Fock spaces on ${\mathbb C}^n$ with the weight function $\varphi$ that \(\varphi \in {\mathcal{C}}^{2}\left( {\mathbb{C}}^{n}\right)\) is real-valued and satisfies $ m{\omega }_{0} \leq d{d}^{c}\varphi \leq M{\omega }_{0} $ for two positive constants \(m\) and \(M\), \({\omega }_{0} = d{d}^{c}{\left| z\right| }^{2}\) is the Euclidean K\"{a}hler form on \({\mathbb{C}}^{n}\), \({d}^{c} = \frac{\sqrt{-1}}{4}\left( {\bar{\partial } - \partial }\right)\). In this paper, we completely characterize those positive Borel measure $\mu$ on ${\mathbb C}^n$ so that the induced Toeplitz operators $T_\mu$ is $r$-summing on $F_{\varphi}^{p}$ for $r \ge 1$.