Bergman projections on weighted Fock spaces in several complex variables - Lv, Xiaofen (Journal of inequalities and applications, 2017)
Let ϕ be a real-valued plurisubharmonic function on C n 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 p th 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 F 2 ( ϕ ) .