scholarly journals Composition operators on Qp spaces

2001 ◽  
Vol 70 (2) ◽  
pp. 161-188 ◽  
Author(s):  
Zengjian Lou
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Function Space ◽  
Composition Operators ◽  
Bloch Space ◽  
Dirichlet Space ◽  
Holomorphic Functions ◽  
Bloch Spaces ◽  
Holomorphic Map ◽  
Analytic Function Space

AbstractA holomorphic map ψ of the unit disk ito itself induces an operator Cψ on holomorphic functions by composition. We characterize bounded and compact composition operators Cψ on Qp spaces, which coincide with the BMOA for p = 1 and Bloch spaces for p > 1. We also give boundedness and compactness characterizations of Cψ from analytic function space X to Qp spaces, X = Dirichlet space D, Bloch space B or B0 = {f: f′ ∈ H∞}.

scholarly journals Composition operators on some Möbius invariant Banach spaces

2000 ◽  
Vol 62 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Shamil Makhmutov ◽  
Maria Tjani
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Unit Disk ◽  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Holomorphic Functions ◽  
Mean Oscillation

We characterise the compact composition operators from any Mobius invariant Banach space to VMOA, the space of holomorphic functions on the unit disk U that have vanishing mean oscillation. We use this to obtain a characterisation of the compact composition operators from the Bloch space to VMOA. Finally, we study some properties of hyperbolic VMOA functions. We show that a function is hyperbolic VMOA if and only if it is the symbol of a compact composition operator from the Bloch space to VMOA.

scholarly journals A New Essential Norm Estimate of Composition Operators from Weighted Bloch Space into -Bloch Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
René E. Castillo ◽  
Julio C. Ramos-Fernández ◽  
Edixon M. Rojas
Keyword(s):  
Weight Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Special Function ◽  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces ◽  
Norm Estimate ◽  
Operator Mapping

Let be any weight function defined on the unit disk and let be an analytic self-map of . In the present paper, we show that the essential norm of composition operator mapping from the weighted Bloch space to -Bloch space is comparable to where for ,   is a certain special function in the weighted Bloch space. As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003).

A NEW ESSENTIAL NORM ESTIMATE OF COMPOSITION OPERATORS FROM α-BLOCH SPACES INTO μ-BLOCH SPACES

2013 ◽  
Vol 24 (14) ◽  
pp. 1350104 ◽  
Author(s):  
JULIO C. RAMOS-FERNÁNDEZ
Keyword(s):  
Weight Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Besov Spaces ◽  
Special Function ◽  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces ◽  
Norm Estimate

Let μ be any weight function defined on the unit disk 𝔻 and let ϕ be an analytic self-map of 𝔻. In this paper, we show that the essential norm of composition operator Cϕ mapping from the α-Bloch space, with α > 0, to μ-Bloch space [Formula: see text] is comparable to [Formula: see text] where, for a ∈ 𝔻, σa is a certain special function in α-Bloch space. As a consequence of our estimate, we extend recent results, about the compactness of composition operators, due to Tjani in [Compact composition operators on Besov spaces, Trans. Amer. Math. Soc.355(11) (2003) 4683–4698] and Malavé Ramírez and Ramos-Fernández in [On a criterion for continuity and compactness of composition operators acting on α-Bloch spaces, C. R. Math. Acad. Sci. Paris351 (2013) 23–26, http://dx.doi.org/10.1016/j.crma.2012.11.013 ].

scholarly journals Differences of weighted differentiation composition operators from α-Bloch space to H∞ space

Filomat ◽  
2019 ◽  
Vol 33 (3) ◽  
pp. 761-772
Author(s):  
Cui Wang ◽  
Ze-Hua Zhou
Keyword(s):  
Unit Disk ◽  
Composition Operators ◽  
Bloch Space ◽  
Holomorphic Functions ◽  
Bounded Holomorphic

This paper characterizes the boundedness and compactness of the differences of weighted differentiation composition operators acting from the ?-Bloch space B? to the space H? of bounded holomorphic functions on the unit disk D.

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 Characterisation of the isometric composition operators on the Bloch space

2005 ◽  
Vol 72 (2) ◽  
pp. 283-290 ◽  
Author(s):  
Flavia Colonna
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Blaschke Product ◽  
Analytic Functions ◽  
Composition Operators ◽  
Bloch Space ◽  
Open Unit ◽  
Open Unit Disk ◽  
Identity Function

In this paper, we characterise the analytic functions ϕ mapping the open unit disk ▵ into itself whose induced composition operator Cϕ: f ↦ f ∘ ϕ is an isometry on the Bloch space. We show that such functions are either rotations of the identity function or have a factorisation ϕ = gB where g is a non-vanishing analytic function from Δ into the closure of ▵, and B is an infinite Blaschke product whose zeros form a sequence{zn} containing 0 and a subsequence satisfying the conditions , and

scholarly journals Norm and Essential Norm of Composition Followed by Differentiation from Logarithmic Bloch Spaces toHμ∞

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Shanli Ye
Keyword(s):  
Lower Bound ◽  
Unit Disk ◽  
Weighted Space ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces

In this note we express the norm of composition followed by differentiationDCφfrom the logarithmic Bloch and the little logarithmic Bloch spaces to the weighted spaceHμ∞on the unit disk and give an upper and a lower bound for the essential norm of this operator from the logarithmic Bloch space toHμ∞.

POWERS OF COMPOSITION OPERATORS: ASYMPTOTIC BEHAVIOUR ON BERGMAN, DIRICHLET AND BLOCH SPACES

2019 ◽  
Vol 108 (3) ◽  
pp. 289-320 ◽  
Author(s):  
W. ARENDT ◽  
I. CHALENDAR ◽  
M. KUMAR ◽  
S. SRIVASTAVA
Keyword(s):  
Asymptotic Behaviour ◽  
Banach Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Dirichlet Space ◽  
Complete Characterization ◽  
Weighted Bergman Spaces ◽  
Bloch Type Space ◽  
Spaces Of Holomorphic Functions

We study the asymptotic behaviour of the powers of a composition operator on various Banach spaces of holomorphic functions on the disc, namely, standard weighted Bergman spaces (finite and infinite order), Bloch space, little Bloch space, Bloch-type space and Dirichlet space. Moreover, we give a complete characterization of those composition operators that are similar to an isometry on these various Banach spaces. We conclude by studying the asymptotic behaviour of semigroups of composition operators on these various Banach spaces.

scholarly journals Geometric properties of composition operators belonging to Schatten classes

2001 ◽  
Vol 26 (4) ◽  
pp. 239-248 ◽  
Author(s):  
Yongsheng Zhu
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Composition Operators ◽  
Schatten Classes ◽  
Geometric Properties ◽  
Image Domain ◽  
Function Mapping

We investigate the connection between the geometry of the image domain of an analytic function mapping the unit disk into itself and the membership of the composition operator induced by this function in the Schatten classes. The purpose is to provide solutions to Lotto's conjectures and show a new compact composition operator which is not in any of the Schatten classes.

scholarly journals A Modified Analytic Function Space Feynman Integral and Its Applications

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Seung Jun Chang ◽  
Jae Gil Choi ◽  
Hyun Soo Chung
Keyword(s):  
Analytic Function ◽  
Function Space ◽  
Feynman Integral ◽  
Integration Formulas ◽  
Generalized Analytic Function ◽  
Analytic Function Space

We analyze the generalized analytic function space Feynman integral and then defined a modified generalized analytic function space Feynman integral to explain the physical circumstances. Integration formulas involving the modified generalized analytic function space Feynman integral are established which can be applied to several classes of functionals.

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