Bergman projections on weighted Fock spaces in several complex variables

摘要

Let ϕ be a real-valued plurisubharmonic function on ℂⁿ whose complex Hessian has uniformly comparable eigenvalues, and let ℱ^p(ϕ) 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(ϕ) to ℱ^p(ϕ) for 1 ≤ p ≤ ∞. As a remark, we claim that Bergman projections are also well defined and bounded on Fock spaces ℱ^p(ϕ) with 0  p  1. We also obtain the estimates for the distance induced by ϕ and the L^p(ϕ)-norm of Bergman kernel for ℱ²(ϕ).