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 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.

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.

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 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 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.

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.

A New Isometric Integral Operator on Bloch Space in the Disk

2012 ◽  
Vol 557-559 ◽  
pp. 2118-2121
Author(s):  
Geng Lei Li
Keyword(s):  
Integral Operator ◽  
Bloch Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

In this paper, we defined a new integral operator and studied the isometric properties on the Bloch space in the disk. we gave a necessary and sufficient condition about it.

scholarly journals M-quasi-hyponormal composition operators

1987 ◽  
Vol 10 (3) ◽  
pp. 621-623
Author(s):  
Pushpa R. Suri ◽  
N. Singh
Keyword(s):  
Composition Operators ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient

A necessary and sufficient condition is obtained forM-quasi-hyponormal composition operators. It has also been proved that the class ofM-quasi-hyponormal composition operators coincides with the class ofM-paranormal composition operators. Existence ofM-hyponormal composition operators which are not hyponormal; andM-quasihyponormal composition operators which are notM-hyponormal and quasi-hyponormal are also shown.

Weighted fractional composition operators on certain function spaces

2019 ◽  
Vol 13 (04) ◽  
pp. 2050082
Author(s):  
D. Borgohain ◽  
S. Naik
Keyword(s):  
Composition Operator ◽  
Fractional Composition ◽  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Function Spaces ◽  
Bloch Spaces ◽  
Type Spaces ◽  
Necessary And Sufficient ◽  
Weighted Type

In this paper, we give some characterizations for the boundedness of weighted fractional composition operator [Formula: see text] from [Formula: see text]-Bloch spaces into weighted type spaces by deriving the bounds of its norm. Also, estimates for essential norm are obtained which gives necessary and sufficient conditions for the compactness of the operator [Formula: see text].

Composition operators between Bergman spaces of logarithmic weights

2015 ◽  
Vol 26 (09) ◽  
pp. 1550068 ◽  
Author(s):  
Ern Gun Kwon ◽  
Jinkee Lee
Keyword(s):  
Integral Representation ◽  
Bergman Space ◽  
Composition Operators ◽  
Counting Function ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Necessary And Sufficient ◽  
Logarithmic Weight

Let [Formula: see text] be the composition operator induced by a holomorphic self-map φ of the open complex unit disk. In this paper, a necessary and sufficient condition for the boundedness of [Formula: see text] from one weighted Bergman space of logarithmic weight into another is described in terms of a growth condition of a generalized counting function for φ. We make use of a new integral representation of a modified counting function which depends on log-convexity of the weight function as well as some estimates for the norm of the weighted Bergman space.

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