scholarly journals Composition operators on some holomorphic Banach function spaces

2009 ◽  
Vol 104 (2) ◽  
pp. 275 ◽  
Author(s):  
A. El-Sayed Ahmed ◽  
M.A. Bakhit
Keyword(s):  
Composition Operator ◽  
Carleson Measure ◽  
Composition Operators ◽  
Bloch Space ◽  
Function Spaces ◽  
Banach Function Spaces

In this paper, we study composition operators on some Möbius invariant Banach function spaces like Bloch and $F(p,q,s)$ spaces. We give a Carleson measure characterization on $F(p,q,s)$ spaces, then we use this Carleson measure characterization of the compact compositions on $F(p,q,s)$ spaces to show that every compact composition operator on $F(p,q,s)$ spaces is compact on a Bloch space. Also, we give conditions to clarify when the converse holds.

scholarly journals On composition operators inQKtype spaces

2007 ◽  
Vol 5 (2) ◽  
pp. 103-122 ◽  
Author(s):  
Marko Kotilainen
Keyword(s):  
Banach Space ◽  
Analytic Function ◽  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Function Spaces ◽  
Analytic Mapping ◽  
Analytic Function Spaces

Letp≥1,q>-2and letK:[0,∞)→[0,∞)be nondecreasing. With a different choice ofp,q,K, the Banach spaceQK(p,q)coincides with many well-known analytic function spaces. Boundedness and compactness of the composition operatorCφfromα-Bloch spaceBαintoQK(p,q)are characterized by a condition depending only on analytic mappingφ:𝔻→𝔻. The same properties are also studied in the caseCφ:QK(p,q)→Bα.

scholarly journals The n-th derivative characterisation of Möbius invariant Dirichlet space

1998 ◽  
Vol 58 (1) ◽  
pp. 43-56 ◽  
Author(s):  
Rauno Aulaskari ◽  
Maria Nowak ◽  
Ruhan Zhao
Keyword(s):  
Carleson Measure ◽  
Bloch Space ◽  
Dirichlet Space ◽  
Function Spaces ◽  
Multiplier Space ◽  
Little Bloch Space ◽  
Special Parameter

In this paper we give the n-th derivative criterion for functions belonging to recently defined function spaces Qp and Qp, 0. For a special parameter value p = 1 this criterion is applied to BMOA and VMOA, and for p > 1 it is applied to the Bloch space and the little Bloch space . Further, a Carleson measure characterisation is given to Qp, and in the last section the multiplier space from Hq into Qp is considered.

scholarly journals Isometric and Closed-Range Composition Operators between Bloch-Type Spaces

2011 ◽  
Vol 2011 ◽  
pp. 1-15
Author(s):  
Nina Zorboska
Keyword(s):  
Holomorphic Function ◽  
Composition Operators ◽  
Function Spaces ◽  
Complete Characterization ◽  
Closed Range ◽  
Different Types ◽  
Type Spaces ◽  
Range Determination

We present an overview of the known results describing the isometric and closed-range composition operators on different types of holomorphic function spaces. We add new results and give a complete characterization of the isometric univalently induced composition operators acting between Bloch-type spaces. We also add few results on the closed-range determination of composition operators on Bloch-type spaces and present the problems that are still open.

Composition operators on μ-Bloch spaces

2009 ◽  
Vol 61 (1) ◽  
pp. 50-75 ◽  
Author(s):  
Huaihui Chen ◽  
Paul Gauthier
Keyword(s):  
Continuous Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Sufficient Conditions ◽  
Positive Continuous Function ◽  
Bloch Spaces ◽  
Bloch Functions ◽  
Necessary And Sufficient

Abstract. Given a positive continuous function μ on the interval 0 < t ≤ 1, we consider the space of so-called μ-Bloch functions on the unit ball. If μ(t ) = t, these are the classical Bloch functions. For μ, we define a metric Fμz (u) in terms of which we give a characterization of μ-Bloch functions. Then, necessary and sufficient conditions are obtained in order that a composition operator be a bounded or compact operator between these generalized Bloch spaces. Our results extend those of Zhang and Xiao.

scholarly journals Weighted Fractional Differentiation Composition Operators from Mixed-Norm Spaces to Weighted-Type Spaces

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
D. Borgohain ◽  
S. Naik
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Open Unit ◽  
Mixed Norm ◽  
Fractional Differentiation ◽  
Mixed Norm Space ◽  
Type Spaces ◽  
Analytic Maps ◽  
Weighted Type

Let 𝔻 be an open unit disc in the complex plane ℂ and let φ:𝔻→𝔻 as well as u:𝔻→ℂ be analytic maps. For an analytic function f(z)=∑n=0∞anzn on 𝔻 the weighted fractional differentiation composition operator is defined as (Dφ,uβf)(z)=u(z)f[β](φ(z)), where β≥0, f[β](z)=∑n=0∞(Γ(n+1+β)/Γ(n+1))anzn, and f0z=fz. In this paper, we obtain a characterization of boundedness and compactness of weighted fractional differentiation composition operator from mixed-norm space Hp,q,ϕ to weighted-type space Hμ∞.

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 Carleson Measure Theorems for Large Hardy-Orlicz and Bergman-Orlicz Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Stéphane Charpentier ◽  
Benoît Sehba
Keyword(s):  
Unit Ball ◽  
Orlicz Space ◽  
Carleson Measure ◽  
Composition Operators ◽  
Orlicz Spaces ◽  
Growth Functions

We characterize those measuresμfor which the Hardy-Orlicz (resp., weighted Bergman-Orlicz) spaceHΨ1(resp.,AαΨ1) of the unit ball ofCNembeds boundedly or compactly into the Orlicz spaceLΨ2(BN¯,μ)(resp.,LΨ2(BN,μ)), when the defining functionsΨ1andΨ2are growth functions such thatL1⊂LΨjforj∈{1,2}, and such thatΨ2/Ψ1is nondecreasing. We apply our result to the characterization of the boundedness and compactness of composition operators fromHΨ1(resp.,AαΨ1) intoHΨ2(resp.,AαΨ2).

scholarly journals Weighted Composition Operators from the Bloch Space and the Analytic Besov Spaces into the Zygmund Space

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Composition Operator ◽  
Besov Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operators ◽  
Zygmund Space ◽  
Weighted Composition ◽  
Special Case

We provide several characterizations of the bounded and the compact weighted composition operators from the Bloch space and the analytic Besov spaces (with ) into the Zygmund space . As a special case, we show that the bounded (resp., compact) composition operators from , , and to coincide. In addition, the boundedness and the compactness of the composition operator can be characterized in terms of the boundedness (resp., convergence to 0, under the boundedness assumption of the operator) of the Zygmund norm of the powers of the symbol.

scholarly journals WEIGHTED COMPOSITION OPERATORS FROM F(p, q, s) TO BLOCH TYPE SPACES ON THE UNIT BALL

2008 ◽  
Vol 19 (08) ◽  
pp. 899-926 ◽  
Author(s):  
ZE-HUA ZHOU ◽  
REN-YU CHEN
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
Type Spaces ◽  
Weighted Composition

Let ϕ(z) = (ϕ1(z),…,ϕn(z)) be a holomorphic self-map of B and ψ(z) a holomorphic function on B, where B is the unit ball of ℂn. Let 0 < p, s < +∞, -n - 1 < q < +∞, q+s > -1 and α ≥ 0, this paper characterizes boundedness and compactness of weighted composition operator Wψ,ϕ induced by ϕ and ψ between the space F(p, q, s) and α-Bloch space [Formula: see text].

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