scholarly journals A note on smoothing properties of the Bergman projection

2016 ◽  
Vol 27 (11) ◽  
pp. 1650087 ◽  
Author(s):  
Sivaguru Ravisankar ◽  
Yunus E. Zeytuncu
Keyword(s):  
Holomorphic Functions ◽  
Bergman Projection ◽  
Bounded Domains ◽  
Satisfy Condition ◽  
Reinhardt Domains ◽  
Smoothing Property

Recently Herbig, McNeal, and Straube have showed that the Bergman projection of conjugate holomorphic functions is smooth up to the boundary on smoothly bounded domains that satisfy condition R. We show that a further smoothing property holds on a family of Reinhardt domains; namely, the Bergman projection of conjugate holomorphic functions is holomorphic past the boundary.

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.

Projections on Bergman Spaces Over Plane Domains

1979 ◽  
Vol 31 (6) ◽  
pp. 1269-1280 ◽  
Author(s):  
Jacob Burbea
Keyword(s):  
Bergman Kernel ◽  
Bergman Spaces ◽  
Holomorphic Functions ◽  
Plane Domain ◽  
Bergman Projection ◽  
Lebesgue Spaces ◽  
Lebesque Measure ◽  
Image Position

Let D be a bounded plane domain and let Lp(D) stand for the usual Lebesgue spaces of functions with domain D, relative to the area Lebesque measure dσ(z) = dxdy. The class of all holomorphic functions in D will be denoted by H(D) and we write Bp(D) = Lp(D) ∩ H(D). Bp(D) is called the Bergman p-space and its norm is given byLet be the Bergman kernel of D and consider the Bergman projection(1.1)It is well known that P is not bounded on Lp(D), p = 1, ∞, and moreover, it can be shown that there are no bounded projections of L∞(Δ) onto B∞(Δ).

scholarly journals On Extremal Problems in Certain New Bergman Type Spaces in Some Bounded Domains inCn

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Romi F. Shamoyan ◽  
Olivera Mihić
Keyword(s):  
Unit Disk ◽  
Bergman Kernel ◽  
Extremal Problems ◽  
Bergman Projection ◽  
Bounded Domains ◽  
Bounded Symmetric Domains ◽  
Siegel Domains ◽  
Type Spaces ◽  
Tube Type ◽  
Homogeneous Domains

Based on recent results on boundedness of Bergman projection with positive Bergman kernel in analytic spaces in various types of domains inCn, we extend our previous sharp results on distances obtained for analytic Bergman type spaces in unit disk to some new Bergman type spaces in Lie ball, bounded symmetric domains of tube type, Siegel domains, and minimal bounded homogeneous domains.

scholarly journals On traces of holomorphic functions on the unit polyball

2009 ◽  
Vol 3 (2) ◽  
pp. 198-211 ◽  
Author(s):  
Romi Shamoyan ◽  
Olivera Mihic
Keyword(s):  
Holomorphic Functions ◽  
Bergman Projection ◽  
Projection Theorem ◽  
Type Classes

In this paper we completely describe traces of holomorphic Bergman classes and Bloch-type classes on polyballs and obtain related estimates generalizing classical Bergman projection theorem.

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