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

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

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