scholarly journals The Multiplication Operator fromF(p,q,s)Spaces tonth Weighted-Type Spaces on the Unit Disk

2012 ◽  
Vol 2012 ◽  
pp. 1-21 ◽  
Author(s):  
Yongmin Liu ◽  
Yanyan Yu
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Multiplication Operator ◽  
Space Of Analytic Functions ◽  
Type Spaces ◽  
Weighted Type

LetH(𝔻)be the space of analytic functions on𝔻andu∈H(𝔻). The boundedness and compactness of the multiplication operatorMufromF(p,q,s),(or  F0(p,q,s))spaces tonth weighted-type spaces on the unit disk are investigated in this paper.

scholarly journals Composition operators fromℬαtoQKtype spaces

2008 ◽  
Vol 6 (1) ◽  
pp. 88-104 ◽  
Author(s):  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Analytic Functions ◽  
Composition Operators ◽  
Nondecreasing Function ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Space Of Analytic Functions ◽  
Type Spaces ◽  
Necessary And Sufficient

Suppose thatϕis an analytic self-map of the unit diskΔ. Necessary and sufficient condition are given for the composition operatorCϕf=fοϕto be bounded and compact fromα-Bloch spaces toQKtype spaces which are defined by a nonnegative, nondecreasing functionk(r)for0≤r<∞. Moreover, the compactness of composition operatorCϕfromℬ0toQKtype spaces are studied, whereℬ0is the space of analytic functions offwithf′∈H∞and‖f‖ℬ0=|f(0)|+‖f′‖∞.

Commutants of composition operators induced by a parabolic linear fractional automorphisms of the unit disk

2012 ◽  
Vol 15 (1) ◽  
Author(s):  
Yuriy Linchuk
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Analytic Functions ◽  
Composition Operators ◽  
Linear Fractional Transformation ◽  
Space Of Analytic Functions ◽  
Continuous Operators

AbstractThe commutant of composition operator induced by a parabolic linear fractional transformation of the unit disk onto itself in the class of linear continuous operators acting on the space of analytic functions is described.

scholarly journals Characterizations of Bloch-Type Spaces of Harmonic Mappings

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Munirah Aljuaid ◽  
Flavia Colonna
Keyword(s):  
Banach Space ◽  
Analytic Functions ◽  
Bloch Space ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Type Spaces ◽  
Growth Space ◽  
Derivatives Of

We study the Banach space BHα (α>0) of the harmonic mappings h on the open unit disk D satisfying the condition supz∈D⁡(1-z2)α(hzz+hz¯z)<∞, where hz and hz¯ denote the first complex partial derivatives of h. We show that several properties that are valid for the space of analytic functions known as the α-Bloch space extend to BHα. In particular, we prove that for α>0 the mappings in BHα can be characterized in terms of a Lipschitz condition relative to the metric defined by dH,α(z,w)=sup⁡{hz-hw:h∈BHα,hBHα≤1}. When α>1, the harmonic α-Bloch space can be viewed as the harmonic growth space of order α-1, while for 0<α<1, BHα is the space of harmonic mappings that are Lipschitz of order 1-α.

scholarly journals On Some Properties of Cowen-Douglas Class of Operators

2018 ◽  
Vol 2018 ◽  
pp. 1-6 ◽  
Author(s):  
Parastoo Heiatian Naeini ◽  
Bahmann Yousefi
Keyword(s):  
Hilbert Space ◽  
Analytic Function ◽  
Essential Spectrum ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Multiplication Operator ◽  
Multiplication Operators ◽  
Space Of Analytic Functions ◽  
Class Operator ◽  
Necessary And Sufficient

We will consider multiplication operators on a Hilbert space of analytic functions on a domainΩ⊂C. For a bounded analytic functionφonΩ, we will give necessary and sufficient conditions under which the complement of the essential spectrum ofMφinφΩbecomes nonempty and this gives conditions for the adjoint of the multiplication operatorMφbelongs to the Cowen-Douglas class of operators. Also, we characterize the structure of the essential spectrum of a multiplication operator and we determine the commutants of certain multiplication operators. Finally, we investigate the reflexivity of a Cowen-Douglas class operator.

scholarly journals A Class of Integral Operators Preserving Subordination and Superordination for Analytic Functions

2012 ◽  
Vol 2012 ◽  
pp. 1-17
Author(s):  
H. A. Al-Kharsani ◽  
N. M. Al-Areefi ◽  
Janusz Sokół
Keyword(s):  
Hypergeometric Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Type Theorem ◽  
Integral Operators ◽  
Gauss Hypergeometric Function ◽  
Open Unit ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Sandwich Type

The purpose of the paper is to investigate several subordination- and superordination-preserving properties of a class of integral operators, which are defined on the space of analytic functions in the open unit disk. The sandwich-type theorem for these integral operators is also presented. Moreover, we consider an application of the subordination and superordination theorem to the Gauss hypergeometric function.

Extremal Problems for the Classes SR-p and TR-p

1990 ◽  
Vol 42 (4) ◽  
pp. 619-645
Author(s):  
Walter Hengartner ◽  
Wojciech Szapiel
Keyword(s):  
Uniform Convergence ◽  
Linear Space ◽  
Unit Disk ◽  
Real Axis ◽  
Analytic Functions ◽  
Dual Space ◽  
Extremal Problems ◽  
Space Of Analytic Functions ◽  
The Real

Let H(D) be the linear space of analytic functions on a domain D of ℂ endowed with the topology of locally uniform convergence and let H‘(D) be the topological dual space of H(D). For domains D which are symmetric with respect to the real axis we use the notation Furthermore, denote by S the set of all univalent mappings f defined on the unit disk Δ which are normalized by f (0) = 0 and f‘(0) =1.

On VMOA for Riemann Surfaces

1988 ◽  
Vol 40 (5) ◽  
pp. 1174-1185 ◽  
Author(s):  
Rauno Aulaskari
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Analytic Functions ◽  
Riemann Surfaces ◽  
Space Of Analytic Functions ◽  
Dirichlet Integral ◽  
Image Position

Let Δ = {z│ │z│ < 1} be the unit disk and f an analytic function in Δ. The Dirichlet integral DΔ(f) of f on Δ is defined byand we denote by AD(Δ) the space of all functions f analytic on Δ for which DΔ(f) < ∞. We denote by BMOA(Δ) the space of analytic functions f in Δ for whichand by VMOA(Δ) the space of those analytic functions f in BMOA(Δ) satisfying the condition

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