scholarly journals Weighted Composition Operators fromH∞to the Bloch Space on the Polydisc

2007 ◽  
Vol 2007 ◽  
pp. 1-13 ◽  
Author(s):  
Songxiao Li ◽  
Stevo Stevic
Keyword(s):  
Holomorphic Function ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Holomorphic Functions ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Necessary And Sufficient ◽  
Bounded Holomorphic

LetDnbe the unit polydisc ofℂn,ϕ(z)=(ϕ1(z),…,ϕn(z))be a holomorphic self-map ofDn, andψ(z)a holomorphic function onDn. LetH(Dn)denote the space of all holomorphic functions with domainDn,H∞(Dn)the space of all bounded holomorphic functions onDn, andB(Dn)the Bloch space, that is,B(Dn)={f∈H(Dn)|‖f‖B=|f(0)|+supz∈Dn∑k=1n|(∂f/∂zk)(z)|(1−|zk|2)<+∞}. We give necessary and sufficient conditions for the weighted composition operatorψCϕinduced byϕ(z)andψ(z)to be bounded and compact fromH∞(Dn)to the Bloch spaceB(Dn).

WEIGHTED COMPOSITION OPERATORS BETWEEN H∞ AND GENERALLY WEIGHTED BLOCH SPACES ON POLYDISKS

2010 ◽  
Vol 21 (05) ◽  
pp. 687-699 ◽  
Author(s):  
HAIYING LI ◽  
PEIDE LIU
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Holomorphic Functions ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Unit Polydisk ◽  
Necessary And Sufficient ◽  
Bounded Holomorphic

Let Un be the unit polydisk of Cn, φ(z) = (φ1(z),φ2(z),…,φn(z)) be a holomorphic self-map of Un and ψ be a holomorphic function on Un. H∞(Un) is the space of all bounded holomorphic functions on Un and by a generally weighted Bloch space we mean [Formula: see text]. We give necessary and sufficient conditions of the boundedness and compactness of the weighted composition operator ψCφ between H∞(Un) and [Formula: see text].

scholarly journals Weighted composition operators from Bloch-type into Bers-type spaces

2021 ◽  
Vol 29 (2) ◽  
pp. 243-250
Author(s):  
HAMID VAEZI ◽  
MOHAMAD NAGHLISAR
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Type Space ◽  
Bloch Type Space ◽  
Type Spaces ◽  
Weighted Composition ◽  
Necessary And Sufficient

In this paper we consider the weighted composition operator uC_{\varphi} from Bloch-type space B^{\alpha} into Bers-type space H_{\beta}^{\infty}, in three cases, \alpha>1, \alpha=1 and \alpha<1. We give the necessary and sufficient conditions for boundedness and compactness of the above operator.

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].

scholarly journals Normal and quasinormal weighted composition operators

1991 ◽  
Vol 33 (3) ◽  
pp. 275-279 ◽  
Author(s):  
James T. Campbell ◽  
Mary Embry-Wardrop ◽  
Richard J. Fleming ◽  
S. K. Narayan
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Necessary And Sufficient

In their paper [1], Campbell and Jamison attempted to give necessary and sufficient conditions for a weighted composition operator on an L2 space to be normal, and to be quasinormal. Those conditions, specifically Theorems I and II of that paper, are not valid (see [2] for precise comments on the other results in that paper). In this paper we present a counterexample to those theorems and state and prove characterizations of quasinormality (Theorem 1 below) and normality (Theorem 2 and Corollary 3 below). We also discuss additional examples and information concerning normal weighted composition operators which contribute to the further understanding of this class.

scholarly journals Non-Weakly Supercyclic Weighted Composition Operators

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Z. Kamali ◽  
K. Hedayatian ◽  
B. Khani Robati
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disc ◽  
Space Of Analytic Functions ◽  
Weighted Composition ◽  
Necessary And Sufficient

We give sufficient conditions under which a weighted composition operator on a Hilbert space of analytic functions is not weakly supercyclic. Also, we give some necessary and sufficient conditions for hypercyclicity and supercyclicity of weighted composition operators on the space of analytic functions on the open unit disc.

scholarly journals Antinormal Weighted Composition Operators

2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Dilip Kumar ◽  
Harish Chandra
Keyword(s):  
Hilbert Space ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Counting Measure ◽  
Power Set ◽  
Weighted Composition ◽  
Necessary And Sufficient ◽  
Positive Integers

Letl2=L2N,μ, whereNis set of all positive integers andμis the counting measure whoseσ-algebra is the power set ofN. In this paper, we obtain necessary and sufficient conditions for a weighted composition operator to be antinormal on the Hilbert spacel2. We also determine a class of antinormal weighted composition operators on Hardy spaceH2D.

Weighted composition operators between Fock spaces ℱ∞(ℂ) and ℱp(ℂ)

2019 ◽  
Vol 30 (03) ◽  
pp. 1950015 ◽  
Author(s):  
Le Hai Khoi ◽  
Le Thi Hong Thom ◽  
Pham Trong Tien
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Connected Components ◽  
Weighted Composition Operators ◽  
Fock Spaces ◽  
Weighted Composition ◽  
Necessary And Sufficient ◽  
Path Connected

In this paper, we establish necessary and sufficient conditions for boundedness and compactness of weighted composition operators acting between Fock spaces [Formula: see text] and [Formula: see text]. We also give complete descriptions of path connected components for the space of composition operators and the space of nonzero weighted composition operators in this context.

scholarly journals Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Banach Space ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Weighted Composition

The logarithmic Bloch spaceBlog⁡is the Banach space of analytic functions on the open unit disk&#x1D53B;whose elementsfsatisfy the condition∥f∥=sup⁡z∈&#x1D53B;(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy spaceHp(with1≤p≤∞) into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mappingHpinto the little logarithmic Bloch space defined as the subspace ofBlog⁡consisting of the functionsfsuch thatlim⁡|z|→1(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|=0.

scholarly journals New additive results for Cauchy dual and MP-inverse of weighted composition operators

Filomat ◽  
2021 ◽  
Vol 35 (7) ◽  
pp. 2215-2230
Author(s):  
Morteza Sohrabi
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Weighted Composition ◽  
Necessary And Sufficient

In this paper, we prove some basic results for Cauchy dual of weighted composition operators. Also we introduce some new classes of operators, called ?-hyponormal, ?-quasi-hyponormal, and we provide necessary and sufficient conditions for Cauchy dual and MP-inverse of weighted composition operators on L2(?) to belong to these classes. In addition, we study the complex symmetry of these types of operators. Moreover, some examples are provided to illustrate the obtained results.

scholarly journals Essential Norms of Weighted Composition Operators from theα-Bloch Space to a Weighted-Type Space on the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Lower And Upper Bounds ◽  
Type Space ◽  
Weighted Composition ◽  
Weighted Type

This paper finds some lower and upper bounds for the essential norm of the weighted composition operator fromα-Bloch spaces to the weighted-type spaceHμ∞on the unit ball for the caseα≥1.

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