scholarly journals Weighted Bergman projections on the Hartogs triangle

2017 ◽  
Vol 446 (1) ◽  
pp. 546-567 ◽  
Author(s):  
Liwei Chen
Keyword(s):  
Hartogs Triangle ◽  
Bergman Projections

Mapping properties of the Bergman projections on elementary Reinhardt domains

2021 ◽  
Vol 71 (4) ◽  
pp. 831-844
Author(s):  
Shuo Zhang
Keyword(s):  
Sobolev Spaces ◽  
Bergman Projection ◽  
Reinhardt Domain ◽  
Reinhardt Domains ◽  
Multi Index ◽  
Bergman Projections

Abstract The elementary Reinhardt domain associated to multi-index k = (k 1, …, k n ) ∈ ℤ n is defined by ℋ ( k ) : = { z ∈ D n : z k   is defined and   | z k | < 1 } . $$\mathcal{H}(\mathbf{k}):=\{z\in\mathbb{D}^n: z^{\mathbf{k}}\ \text{is defined and}\ |z^{\mathbf{k}}|<1\}.$$ In this paper, we study the mapping properties of the associated Bergman projection on L p spaces and L p Sobolev spaces of order ≥ 1.

scholarly journals Sobolev and Lipschitz estimates for weighted Bergman projections

1997 ◽  
Vol 147 ◽  
pp. 147-178 ◽  
Author(s):  
Der-Chen Chang ◽  
Bao Qin Li
Keyword(s):  
Finite Type ◽  
Convex Domain ◽  
Functional Calculus ◽  
Smooth Boundary ◽  
Lipschitz Estimates ◽  
Pseudo Convex Domain ◽  
Pseudo Convex ◽  
Bergman Projections ◽  
Distance To The Boundary

AbstractLet Ω be a bounded, decoupled pseudo-convex domain of finite type in ℂn with smooth boundary. In this paper, we generalize results of Bonami-Grellier [BG] and Bonami-Chang-Grellier [BCG] to study weighted Bergman projections for weights which are a power of the distance to the boundary. We define a class of operators of Bergman type for which we develop a functional calculus. Then we may obtain Sobolev and Lipschitz estimates, both of isotropic and anisotropic type, for these projections.

Sobolev regularity of the $$\overline{\partial }$$ -equation on the Hartogs triangle

2012 ◽  
Vol 356 (1) ◽  
pp. 241-258 ◽  
Author(s):  
Debraj Chakrabarti ◽  
Mei-Chi Shaw
Keyword(s):  
Sobolev Regularity ◽  
Hartogs Triangle
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