Absolutely Summing Toeplitz operators on Fock spaces

Abstract

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 $r \ge 1$.