scholarly journals Solution of Extremal Problems in Bergman Spaces Using the Bergman Projection

2014 ◽  
Vol 14 (1) ◽  
pp. 35-61
Author(s):  
Timothy Ferguson
Keyword(s):  
Bergman Spaces ◽  
Extremal Problems ◽  
Bergman Projection

scholarly journals On some extremal problems in Bergman spaces in weakly pseudoconvex domains

2018 ◽  
Vol 26 (2) ◽  
pp. 83-97
Author(s):  
Romi F. Shamoyan ◽  
Olivera R. Mihić
Keyword(s):  
Distance Function ◽  
Bergman Kernel ◽  
Additional Condition ◽  
Bergman Spaces ◽  
Representation Formula ◽  
Extremal Problems ◽  
Bergman Projection ◽  
Pseudoconvex Domains ◽  
Weakly Pseudoconvex

AbstractWe consider and solve extremal problems in various bounded weakly pseudoconvex domains in ℂn based on recent results on boundedness of Bergman projection with positive Bergman kernel in Bergman spaces $A_\alpha ^p$ in such type domains. We provide some new sharp theorems for distance function in Bergman spaces in bounded weakly pseudoconvex domains with natural additional condition on Bergman representation formula.

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 Embedding relations and boundedness of the multifunctional operators in tube domains over symmetric cones

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 109-126 ◽  
Author(s):  
Milos Arsenovic ◽  
Romi Shamoyan
Keyword(s):  
Hardy Spaces ◽  
Bergman Spaces ◽  
Bergman Projection ◽  
Symmetric Cones ◽  
Mixed Norm ◽  
Sufficient Condition ◽  
General Sufficient Condition ◽  
Tube Domains

We obtain a new general sufficient condition for the continuity of the Bergman projection in tube domains over symmetric cones using multifunctional embeddings. We also obtain some sharp embedding relations between the generalized Hilbert-Hardy spaces and the mixed-norm Bergman spaces in this setting.

Extremal Problems for Nonvanishing Functions in Bergman Spaces

2005 ◽  
pp. 59-86 ◽  
Author(s):  
Dov Aharonov ◽  
Catherine Bénéteau ◽  
Dmitry Khavinson ◽  
Harold Shapiro
Keyword(s):  
Bergman Spaces ◽  
Extremal Problems

scholarly journals Toeplitz operators on Bergman spaces of polygonal domains

2019 ◽  
Vol 62 (4) ◽  
pp. 1115-1136 ◽  
Author(s):  
Paula Mannersalo
Keyword(s):  
Connected Domain ◽  
Toeplitz Operators ◽  
Bergman Spaces ◽  
Sufficient Conditions ◽  
Bergman Projection ◽  
Polygonal Domains ◽  
Simply Connected Domain ◽  
Whitney Decomposition ◽  
Polygonal Boundary ◽  
Simply Connected

AbstractWe study the boundedness of Toeplitz operators with locally integrable symbols on Bergman spaces Ap(Ω), 1 < p < ∞, where Ω ⊂ ℂ is a bounded simply connected domain with polygonal boundary. We give sufficient conditions for the boundedness of generalized Toeplitz operators in terms of ‘averages’ of symbol over certain Cartesian squares. We use the Whitney decomposition of Ω in the proof. We also give examples of bounded Toeplitz operators on Ap(Ω) in the case where polygon Ω has such a large corner that the Bergman projection is unbounded.

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