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Sobolev and Lipschitz estimates for weighted Bergman projections. (English) Zbl 0896.32002

Let \(\Omega\) be a bounded, decoupled pseudo-convex domain of finite type in \(\mathbb{C}^n\) with smooth boundary.
The authors generalize the results of Bonami-Grellier as well as Bonami-Chang-Grellier to study weighted Bergman projections for weights which are a power of the distance to the boundary. Using functional calculus on a class of operators of Bergman type, we may obtain Sobolev and Lipschitz estimates, both of isotropic and non-isotropic type, for these projections.

MSC:

32A22 Nevanlinna theory; growth estimates; other inequalities of several complex variables
32A37 Other spaces of holomorphic functions of several complex variables (e.g., bounded mean oscillation (BMOA), vanishing mean oscillation (VMOA))
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