  We prove upper pointwise estimates for the Bergman kernel of the weighted
Fock space of entire functions in $L^2(e^{-2\phi})$ where $\phi$ is a
subharmonic function with $\Delta \phi$ a doubling measure. We derive estimates
for the canonical solution operator to the inhomogeneous Cauchy-Riemann
equation and we characterize the compactness of this operator in terms of
$\Delta \phi$.

Complex Variables