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 $r \ge 1$.