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A Note on weighted Composition Operators on the weighted Bergman space

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Acta Mathematica Sinica,English Series 2015年第6期31卷 947-952页

作者： Lian Kuo ZHAO Sheng Zhao HOU School of Mathematics and Computer Science Shanxi Normal University School of Mathematics Science Soochow University

This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space on... 详细信息

关键词： weighted Bergman space weighted composition operator boundedness finite Blaschke product

Little Hankel Operators on the weighted Bergman space of the Unit Ball

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Communications in Mathematical Research 2010年第4期26卷 304-312页

作者： ZHANG KAN LU YU-FENG LIU CHAO-MEI School of Mathematical Sciences Dalian University of TechnologyDalian116024 College of Sciences Shenyang Agricultural UniversityShenyang110866 School of Science Dalian Jiaotong UniversityDalian116028

In this paper we mainly consider little Hankel operators with squareintegrable symbols on the weighted Bergman spaces of the unit ball.We obtain that Schatten class of little Hankel operators is equivalent to Schatten class of positive Toeplitz operators under the conditions that SMO（f） ∈ L p/2 （B n,dλ） and 2 ≤ p ∞,which is very important to research the relation between Toeplitz operators and little Hankel operators.

关键词： weighted Bergman space little Hankel operator unit ball

单位球加权bergman空间上的Berezin变换与径向算子（英文）

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Chinese Quarterly Journal of Mathematics 2015年第1期30卷 47-54页

作者：鲁美麟李德生关洪岩 Department of Mathematics Shenyang Normal University

In this paper, we analyze a class of bounded radial operators on the weighted Bergman space A2α(Bn, d Vα), we get that these kinds of operators are diagonal with respect to the standard orthonomal basis. We also investigate the connection between compactness of operators and the boundary behaviour of the corresponding Berezin transform. We further study a special class of radial operators, i.e., Toeplitz operators with a radial L1 symbol.

关键词： weighted Bergman space Berezin transform Radial operators Toeplitz operators

Bounded Hankel Products on the weighted Bergman space

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Northeastern Mathematical Journal 2006年第2期22卷 127-130页

作者：卢玉峰尚书霞纪友清 Department of Applied Mathematics Dalian University of Technology Dalian 116024

1 Introduction The bergman space Aα^2 is the space of analytic functions on a plane domain D which are square integrable with respect to the measure.

关键词： Hankel product Haplitz product weighted Bergman space

The Root Operator on Invariant Subspaces of the weighted Bergman space

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Journal of Mathematical Research and Exposition 2010年第1期30卷 54-66页

作者： Xiao Yang ZHOU Xiu Ying SHI Yu Feng LU School of Mathematical Science Dalian University of Technology Liaoning 116024 P. R. China School of Continuing Education Chifeng University Inner Mongolia 024000 P. R. China

In this paper, for an invariant subspace I of the weighted Bergman space, the weighted root operator is defined. We study the weighted root operator and obtain its fundamental properties when the invariant subspace I ... 详细信息

关键词： root operator index weighted Bergman space invariant subspace.

MEAN APPROXIMATION BY DILATATIONS IN bergman spaceS ON THE UPPER HALF-PLANE

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数学物理学报:B辑英文版 2023年第5期43卷 2204-2214页

作者： Ali ABKAR Department of Pure Mathematics Faculty of ScienceImam Khomeini International UniversityQazvin 34149Iran

We study sufficient conditions on radial and non-radial weight functions on the upper half-plane that guarantee norm approximation of functions in weighted bergman,weighted Dirichlet,and weighted Besov spaces on the u... 详细信息

关键词： mean approximation dilatation non-radial weight angular weight weighted Bergman space weighted Besov space

HYPONORMALITY OF BLOCK TOEPLITZ OPERATORS ON THE weighted Bergman spaceS

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Acta Mathematica Scientia 2017年第6期37卷 1695-1704页

作者： Jongrak LEE Institute of Mathematical Sciences Ewha Womans UniversitySeoul 120-750Republic of Korea

In this paper we consider the block Toeplitz operators TФ on the weighted Bergman space A2α（D, Cn） and we give a necessary and sufficient condition for the hyponor-mality of block Toeplitz operators with symbol in... 详细信息

关键词： block Toeplitz operators hyponormal weighted Bergman space

Hankel operators on exponential bergman spaces

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Science China Mathematics 2022年第2期65卷 421-442页

作者： Zhangjian Hu Jordi Pau Department of Mathematics Huzhou UniversityHuzhou 313000China Departament de Matematiques i Informatica Universitat de BarcelonaBarcelona 08007Spain

We completely describe the boundedness and compactness of Hankel operators with general symbols acting on bergman spaces with exponential type weights.

关键词： weighted Bergman space Hankel operator ?-equation

Composition operators on weighted Bergman spaces induced by doubling weights

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Science China Mathematics 2024年第7期67卷 1571-1598页

作者： Xin Guo Maofa Wang School of Mathematics and Statistics Wuhan University

Given a doubling weight ω on the unit disk D, let A_ωpbe the space of all the holomorphic functions f, where ∥f ∥A_ωp:=( ∫D|f(z)|pω(z)dA(z))1/p< ∞.We completely characterize the topological connectedness of th... 详细信息

Given a doubling weight ω on the unit disk D, let A_ωpbe the space of all the holomorphic functions f, where ∥f ∥A_ωp:=( ∫D|f(z)|pω(z)dA(z))1/pweighted Bergman space. In addition, we completely describe the central compactness of any finite linear combinations of composition operators on A_ωpin three terms: a Julia-Carathéodory-type function-theoretic characterization, a power-type characterization, and a Carleson-type measure-theoretic characterization.

关键词： composition operator linear combination linearly connected weighted Bergman space doubling weight