Bergman projections on weighted Fock spaces in several complex variables

Let ϕ be a real-valued plurisubharmonic function on ${\mathbb {C}}^{n}$ whose complex Hessian has uniformly comparable eigenvalues, and let $\mathcal{F}^{p}(\phi)$ be the Fock space induced by ϕ. In this paper, we conclude that the Bergman projection is bounded from the pth Lebesgue space $L^{p}(\phi )$ to $\mathcal{F}^{p}(\phi)$ for $1\leq p \leq\infty$ . As a remark, we claim that Bergman projections are also well defined and bounded on Fock spaces $\mathcal{F}^{p}(\phi)$ with $0< p<1$ . We also obtain the estimates for the distance induced by ϕ and the $L^{p}(\phi)$ -norm of Bergman kernel for $\mathcal{F}^{2}(\phi)$ .