2020
DOI: 10.1017/s0004972719001424
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Regularity of the Weighted Bergman Projection on the Fock–bargmann–hartogs Domain

Abstract: The Fock-Bargmann-Hartogs domain D n,m (µ) is defined bywhere µ > 0. The Fock-Bargmann-Hartogs domain D n,m (µ) is an unbounded strongly pseudoconvex domain with smooth real-analytic boundary. In this paper, we first compute the weighted Bergman kernel of D n,m (µ) with respect to the weight (−ρ) α , where ρ(z, w) := w 2 − e −µ z 2 is a defining function for D n,m (µ) and α > −1. Then, for p ∈ [1, ∞), we show that the corresponding weighted Bergman projection P Dn,m(µ),(−ρ) α is unbounded on L p (D n,m (µ), (−… Show more

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