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 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.

The Bergman Projection on Weighted Norm Spaces

1980 ◽  
Vol 32 (4) ◽  
pp. 979-986 ◽  
Author(s):  
Jacob Burbea
Keyword(s):  
Unit Disk ◽  
Bergman Kernel ◽  
Plane Domain ◽  
Bergman Projection ◽  
Weighted Norm ◽  
Multiply Connected Domains ◽  
Multiply Connected ◽  
Muckenhoupt Condition ◽  
Image Position ◽  
Interesting Identity

Quite recently Bekollé and Bonami [1] have characterized the weighted measures λ on the unit disk Δ for which the Bergman projection is bounded on Lp(Δ : λ), 1 < p < ∞. Our methods in [4] can be applied to even extend their result by replacing the unit disk with multiply connected domains. This is done via a rather interesting identity between the Bergman kernel and its “adjoint” [2]. As a corollary of our result we obtain a generalization of a result due to Shikhvatov [7].Let D be a bounded plane domain and let λ be a positive locally integrate function in D. λ is said to belong to Mp(D) (1 < p < ∞) if it satisfies the Muckenhoupt condition:where the supremum is taken over all sectors V ⊂ D, dσ is the area Lebesgue measure and |V| = σ(V).

scholarly journals L∞-Estimates of the Bergman projection in the Lie ball ofℂn

2011 ◽  
Vol 9 (2) ◽  
pp. 109-128 ◽  
Author(s):  
Cyrille Nana
Keyword(s):  
Bergman Projection ◽  
The Other ◽  
Bounded Domains ◽  
Cayley Transform ◽  
Bounded Symmetric Domains ◽  
Bergman Projections

In this paper, we consider estimates with loss for the Bergman projections of bounded symmetric domains ofℂnin their Harish-Chandra realizations. This paper is twofold: on one side we develop transfer methods between these bounded domains and their Cayley transform; on the other side we give a new range ofqsuch that the Bergman projection is bounded fromL∞(ℬn)toLq(ℬn)whereℬnis the Lie ball ofℂn.

scholarly journals On some new sharp embedding theorems for multifunctional Herz-type and Bergman-type spaces in pseudoconvex domains

Filomat ◽  
2019 ◽  
Vol 33 (17) ◽  
pp. 5677-5690 ◽  
Author(s):  
Romi Shamoyan ◽  
Olivera Mihic
Keyword(s):  
Bergman Kernel ◽  
Pseudoconvex Domains ◽  
Symmetric Cones ◽  
Mixed Norm ◽  
Embedding Theorems ◽  
Bounded Symmetric Domains ◽  
Strongly Pseudoconvex Domains ◽  
Type Spaces

We introduce new multifunctional mixed norm analytic Herz-type spaces in strongly pseudoconvex domains and provide new sharp embedding theorems for them. Some results are new even in case of onefunctional holomorphic spaces. Some new related sharp results for new multifunctional Bergman-type spaces will be also provided under one condition on Bergman kernel. Similar results with similar proofs in unbounded tubular domains over symmetric cones and bounded symmetric domains will be also shortly mentioned.

scholarly journals Bloch-Type Spaces of Minimal Surfaces

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Guanghua He ◽  
Xi Fu ◽  
Hancan Zhu
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Minimal Surfaces ◽  
Lipschitz Functions ◽  
Type Spaces

We study Bloch-type spaces of minimal surfaces from the unit disk D into Rn and characterize them in terms of weighted Lipschitz functions. In addition, the boundedness of a composition operator Cϕ acting between two Bloch-type spaces is discussed.

scholarly journals The Multiplication Operator fromF(p,q,s)Spaces tonth Weighted-Type Spaces on the Unit Disk

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yongmin Liu ◽  
Yanyan Yu
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Multiplication Operator ◽  
Space Of Analytic Functions ◽  
Type Spaces ◽  
Weighted Type

LetH(&#x1D53B;)be the space of analytic functions on&#x1D53B;andu∈H(&#x1D53B;). The boundedness and compactness of the multiplication operatorMufromF(p,q,s),(or  F0(p,q,s))spaces tonth weighted-type spaces on the unit disk are investigated in this paper.

KORÁNYI’S LEMMA FOR HOMOGENEOUS SIEGEL DOMAINS OF TYPE II. APPLICATIONS AND EXTENDED RESULTS

2014 ◽  
Vol 90 (1) ◽  
pp. 77-89 ◽  
Author(s):  
DAVID BÉKOLLÉ ◽  
HIDEYUKI ISHI ◽  
CYRILLE NANA
Keyword(s):  
Functional Analysis ◽  
Bergman Kernel ◽  
Atomic Decomposition ◽  
Bergman Spaces ◽  
Decomposition Theorem ◽  
Interpolation Theorem ◽  
Type Ii ◽  
Siegel Domain ◽  
Homogeneous Case ◽  
Siegel Domains

AbstractWe show that the modulus of the Bergman kernel $\def \xmlpi #1{}\def \mathsfbi #1{\boldsymbol {\mathsf {#1}}}\let \le =\leqslant \let \leq =\leqslant \let \ge =\geqslant \let \geq =\geqslant \def \Pr {\mathit {Pr}}\def \Fr {\mathit {Fr}}\def \Rey {\mathit {Re}}B(z, \zeta )$ of a general homogeneous Siegel domain of type II is ‘almost constant’ uniformly with respect to $z$ when $\zeta $ varies inside a Bergman ball. The control is expressed in terms of the Bergman distance. This result was proved by A. Korányi for symmetric Siegel domains of type II. Subsequently, R. R. Coifman and R. Rochberg used it to establish an atomic decomposition theorem and an interpolation theorem by functions in Bergman spaces $A^p$ on these domains. The atomic decomposition theorem and the interpolation theorem are extended here to the general homogeneous case using the same tools. We further extend the range of exponents $p$ via functional analysis using recent estimates.

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).

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