scholarly journals BOUNDED COMPOSITION OPERATORS FROM THE BERGMAN SPACE TO THE HARDY SPACE

2014 ◽  
Vol 51 (4) ◽  
pp. 1005-1013
Author(s):  
Kazuhiro Kasuga ◽  
Takahiko Nakazi
Keyword(s):  
Hardy Space ◽  
Bergman Space ◽  
Composition Operators

Composition Operators Induced by Analytic Maps to the Polydisk

2012 ◽  
Vol 64 (6) ◽  
pp. 1329-1340 ◽  
Author(s):  
Kei Ji Izuchi ◽  
Quang Dieu Nguyen ◽  
Shûichi Ohno
Keyword(s):  
Hardy Space ◽  
Unit Disk ◽  
Bergman Space ◽  
Composition Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Analytic Maps

Abstract We study properties of composition operators induced by symbols acting from the unit disk to the polydisk. This result will be involved in the investigation of weighted composition operators on the Hardy space on the unit disk and, moreover, be concerned with composition operators acting from the Bergman space to the Hardy space on the unit disk.

Approximation numbers of composition operators on the Hardy and Bergman spaces of the ball and of the polydisk

2017 ◽  
Vol 165 (1) ◽  
pp. 69-91 ◽  
Author(s):  
FRÉDÉRIC BAYART ◽  
DANIEL LI ◽  
HERVÉ QUEFFÉLEC ◽  
LUIS RODRÍGUEZ–PIAZZA
Keyword(s):  
Hardy Space ◽  
Bergman Space ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Approximation Numbers ◽  
Hardy And Bergman Spaces

AbstractWe give general estimates for the approximation numbers of composition operators on the Hardy space on the ball Bd and the polydisk ${\mathbb D}$d and of composition operators on the Bergman space on the polydisk.

scholarly journals Ограниченные композиционные операторы на весовых функциональных пространствах на единичном круге

2020 ◽  
Author(s):  
S. Hua ◽  
L.H. Khoi ◽  
P.T. Tien
Keyword(s):  
Hardy Space ◽  
Unit Disk ◽  
Bergman Space ◽  
Functional Properties ◽  
General Class ◽  
Composition Operators ◽  
Dirichlet Space ◽  
Holomorphic Functions ◽  
Sufficient Condition ◽  
Weight Sequence

We introduce a general class of weighted spaces $\calH(\beta)$ of holomorphic functions in the unit disk $\mathbb{D}$, which contains several classical spaces, such as Hardy space, Bergman space, Dirichlet space. We~characterize boundedness of composition operators $C_{\varphi}$ induced by affine and monomial symbols $\varphi$ on these spaces $\calH(\beta)$. We also establish a sufficient condition under which the operator $C_{\varphi}$ induced by the symbol $\varphi$ with relatively compact image $\varphi(\mathbb{D})$ in $\mathbb{D}$ is bounded on $\calH(\beta)$. Note that in the setting of $\calH(\beta)$, the characterizations of boundedness of composition operators $C_{\varphi}$ depend closely not only on functional properties of the symbols $\varphi$ but also on the behavior of the weight sequence $\beta$.

scholarly journals Compact Differences of Composition Operators on Bergman Spaces Induced by Doubling Weights

2021 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä ◽  
Fanglei Wu
Keyword(s):  
Bergman Space ◽  
Open Problem ◽  
Lebesgue Space ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Doubling Weights ◽  
The Way

AbstractBounded and compact differences of two composition operators acting from the weighted Bergman space $$A^p_\omega $$ A ω p to the Lebesgue space $$L^q_\nu $$ L ν q , where $$0<q<p<\infty $$ 0 < q < p < ∞ and $$\omega $$ ω belongs to the class "Equation missing" of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proofs a new description of q-Carleson measures for $$A^p_\omega $$ A ω p , with $$p>q$$ p > q and "Equation missing", involving pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_\alpha $$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights. The case "Equation missing" is also briefly discussed and an open problem concerning this case is posed.

scholarly journals COMPOSITION OPERATORS BELONGING TO SCHATTEN CLASS 𝒮p

2010 ◽  
Vol 81 (3) ◽  
pp. 465-472
Author(s):  
CHENG YUAN ◽  
ZE-HUA ZHOU
Keyword(s):  
Bergman Space ◽  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Schatten Class

AbstractWe investigate the composition operators Cφ acting on the Bergman space of the unit disc D, where φ is a holomorphic self-map of D. Some new conditions for Cφ to belong to the Schatten class 𝒮p are obtained. We also construct a compact composition operator which does not belong to any Schatten class.

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