Bergman projections on weighted Fock spaces in several complex variables

Abstract

Let ϕ be a real-valued plurisubharmonic function on whose complex Hessian has uniformly comparable eigenvalues, and let be the Fock space induced by ϕ. In this paper, we conclude that the Bergman projection is bounded from the pth Lebesgue space to for . As a remark, we claim that Bergman projections are also well defined and bounded on Fock spaces with . We also obtain the estimates for the distance induced by ϕ and the -norm of Bergman kernel for .

Boundedness and Compactness of Hankel Operators on Large Fock Space

“…Recently, the research on the weighted Fock space has been gradually improved. Lv [2] obtained characterizations on the boundedness of the Bergman projection. Arroussi and Tong [3] gave the L p ðϕÞ-norm estimation of the Bergman kernel and studied the boundedness, compactness, and Schatten class membership of the weighted composition operators.…”

“…Moreover, P is bounded from L p ðϕÞ to F p ðϕÞ and Pg = g for any g ∈ F p ðϕÞ when 1 ≤ p < ∞. See [2,4] for more details. From [4], we know that…”