Some spectral properties of the canonical solution operator to $\bar{\mathrm{\partial }}$ on weighted Fock spaces

We characterize the Schatten class membership of the canonical solution operator to $\bar{\mathrm{\partial }}$ acting on $L^2(e^{-2\varphi })$, where $\varphi$ is a subharmonic function with $\mathrm{\Delta }\varphi$ a doubling measure. The obtained characterization is in terms of $\mathrm{\Delta }\varphi$. As part of our approach, we study Hankel operators with anti-analytic symbols acting on the corresponding Fock space of entire functions in $L^2(e^{-2\varphi })$.