We will prove size estimates of the Bergman kernel for the generalized Fock space ${\mathcal{F}}^2_{\varphi}$, where ${\varphi}$ belongs to the class $\mathcal{W} $. The main tool for the proof is to use the estimate on the canonical solution to the $...
We will prove size estimates of the Bergman kernel for the generalized Fock space ${\mathcal{F}}^2_{\varphi}$, where ${\varphi}$ belongs to the class $\mathcal{W} $. The main tool for the proof is to use the estimate on the canonical solution to the ${\bar{\partial}}$-equation. We use Delin's weighted $L^2$-estimate ([3], [6]) for it.