\(L^{p}\) Estimates for the Bergman Projection on Generalized Fock Spaces

We obtain \(L^{p}\) $L^p$ bounds for the Bergman projection \(P_{\varphi }\) $P_{\phi }$ on \(\mathbb {C}^{n}\) ${\mathbb{C}}^n$ for a class of weights \(\varphi \) $\phi$ whose complex Hessian has comparable eigenvalues. This relies on an extension of the estimate on the Bergman kernel obtained previously by Dall’Ara.