## 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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### References:

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