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′‖∞.

scholarly journals Some results on composition operators onℓ2

1979 ◽  
Vol 2 (1) ◽  
pp. 29-34 ◽  
Author(s):  
R. K. Singh ◽  
D. K. Gupta ◽  
B. S. Komal
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Bounded Operator ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

A necessary and sufficient condition for a bounded operator to be a composition operator is investigated in this paper. Normal, quasi-hyponormal, paranormal composition operators are characterised.

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 Composition operators

1978 ◽  
Vol 18 (3) ◽  
pp. 439-446 ◽  
Author(s):  
R.K. Singh ◽  
B.S. Komal
Keyword(s):  
Composition Operator ◽  
Unit Disc ◽  
Composition Operators ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Closed Unit Disc ◽  
Necessary And Sufficient ◽  
Made In

A study of centered composition operators on l2 is made in this paper. Also the spectrum of surjective composition operators is computed. A necessary and sufficient condition is obtained for the closed unit disc to be the spectrum of a surjective composition operator.

Boundedness from Below of Composition Operators on α-Bloch Spaces

2008 ◽  
Vol 51 (2) ◽  
pp. 195-204 ◽  
Author(s):  
Huaihui Chen ◽  
Paul Gauthier
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Bloch Spaces ◽  
Necessary And Sufficient ◽  
Bounded Below

AbstractWe give a necessary and sufficient condition for a composition operator on an α-Bloch space with α ≥ 1 to be bounded below. This extends a known result for the Bloch space due to P. Ghatage, J. Yan, D. Zheng, and H. Chen.

scholarly journals Locally Lipschitz Composition Operators in Space of the Functions of BoundedκΦ-Variation

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Odalis Mejía ◽  
Nelson José Merentes Díaz ◽  
Beata Rzepka
Keyword(s):  
Lipschitz Condition ◽  
Composition Operator ◽  
Composition Operators ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Local Lipschitz Condition ◽  
Locally Lipschitz ◽  
Necessary And Sufficient

We give a necessary and sufficient condition on a functionh:R→Runder which the nonlinear composition operatorH, associated with the functionh,Hu(t)=h(u(t)), acts in the spaceκΦBV[a,b]and satisfies a local Lipschitz condition.

scholarly journals On a Class of Composition Operators on Bergman Space

2007 ◽  
Vol 2007 ◽  
pp. 1-11
Author(s):  
Namita Das ◽  
R. P. Lal ◽  
C. K. Mohapatra
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Measurable Function ◽  
Analytic Functions ◽  
Composition Operators ◽  
Linear Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Bounded Linear

Let&#x1D53B;={z∈ℂ:|z|<1}be the open unit disk in the complex planeℂ. LetA2(&#x1D53B;)be the space of analytic functions on&#x1D53B;square integrable with respect to the measuredA(z)=(1/π)dx dy. Givena∈&#x1D53B;andfany measurable function on&#x1D53B;, we define the functionCafbyCaf(z)=f(ϕa(z)), whereϕa∈Aut(&#x1D53B;). The mapCais a composition operator onL2(&#x1D53B;,dA)andA2(&#x1D53B;)for alla∈&#x1D53B;. Letℒ(A2(&#x1D53B;))be the space of all bounded linear operators fromA2(&#x1D53B;)into itself. In this article, we have shown thatCaSCa=Sfor alla∈&#x1D53B;if and only if∫&#x1D53B;S˜(ϕa(z))dA(a)=S˜(z), whereS∈ℒ(A2(&#x1D53B;))andS˜is the Berezin symbol of S.

scholarly journals Boundedness of composition operators on Morrey spaces and weak Morrey spaces

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Naoya Hatano ◽  
Masahiro Ikeda ◽  
Isao Ishikawa ◽  
Yoshihiro Sawano
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Morrey Spaces ◽  
Characteristic Functions ◽  
Sufficient Condition ◽  
Specific Function ◽  
Necessary And Sufficient Condition ◽  
Lebesgue Spaces ◽  
Necessary And Sufficient ◽  
Weak Morrey Spaces

AbstractIn this study, we investigate the boundedness of composition operators acting on Morrey spaces and weak Morrey spaces. The primary aim of this study is to investigate a necessary and sufficient condition on the boundedness of the composition operator induced by a diffeomorphism on Morrey spaces. In particular, detailed information is derived from the boundedness, i.e., the bi-Lipschitz continuity of the mapping that induces the composition operator follows from the continuity of the composition mapping. The idea of the proof is to determine the Morrey norm of the characteristic functions, and employ a specific function composed of a characteristic function. As this specific function belongs to Morrey spaces but not to Lebesgue spaces, the result reveals a new phenomenon not observed in Lebesgue spaces. Subsequently, we prove the boundedness of the composition operator induced by a mapping that satisfies a suitable volume estimate on general weak-type spaces generated by normed spaces. As a corollary, a necessary and sufficient condition for the boundedness of the composition operator on weak Morrey spaces is provided.

scholarly journals QKtype spaces of analytic functions

2006 ◽  
Vol 4 (1) ◽  
pp. 73-84 ◽  
Author(s):  
Hasi Wulan ◽  
Jizhen Zhou
Keyword(s):  
Unit Disk ◽  
Analytic Functions ◽  
Sufficient Conditions ◽  
Nondecreasing Function ◽  
Necessary And Sufficient Conditions ◽  
Type Space ◽  
Necessary And Sufficient ◽  
Spaces Of Analytic Functions

For a nondecreasing functionK:[0,8)?[0,8)and0<p<8,-2<q<8, we introduceQK(p,q), aQKtype space of functions analytic in the unit disk and study the characterizations ofQK(p,q). Necessary and sufficient conditions onKsuch thatQK(p,q)become some known spaces are given.

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(&#x1D53B;)be the space of analytic functions on&#x1D53B;andu∈H(&#x1D53B;). 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 Certain subclasses of analytic functions involving complex order

Filomat ◽  
2008 ◽  
Vol 22 (2) ◽  
pp. 115-122 ◽  
Author(s):  
T.N. Shanmugam ◽  
S. Sivasubramanian ◽  
B.A. Frasin
Keyword(s):  
Analytic Functions ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Complex Order ◽  
Necessary And Sufficient ◽  
Class Of Functions

In the present investigation, we consider an unified class of functions of complex order. Necessary and sufficient condition for functions to be in this class is obtained. The results obtained in this paper generalizes the results obtained by Srivastava and Lashin [10], and Ravichandran et al. [4]. .

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