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 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′‖∞.

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 The weak law of large numbers for nonnegative summands

2018 ◽  
Vol 50 (A) ◽  
pp. 241-252
Author(s):  
Eugene Seneta
Keyword(s):  
Branching Process ◽  
Law Of Large Numbers ◽  
Random Variables ◽  
Sufficient Condition ◽  
Specific Function ◽  
Slowly Varying Function ◽  
Necessary And Sufficient Condition ◽  
Large Numbers ◽  
Norming Sequence ◽  
Necessary And Sufficient

Abstract Khintchine's (necessary and sufficient) slowly varying function condition for the weak law of large numbers (WLLN) for the sum of n nonnegative, independent and identically distributed random variables is used as an overarching (sufficient) condition for the case that the number of summands is more generally [cn],cn→∞. Either the norming sequence {an},an→∞, or the number of summands sequence {cn}, can be chosen arbitrarily. This theorem generalizes results from a motivating branching process setting in which Khintchine's sufficient condition is automatically satisfied. A second theorem shows that Khintchine's condition is necessary for the generalized WLLN when it holds with cn→∞ and an→∞. Theorem 3, which is known, gives a necessary and sufficient condition for Khintchine's WLLN to hold with cn=n and an a specific function of n; it is extended to general cn subject to a growth restriction in Theorem 4. Section 6 returns to the branching process setting.

A note on the Stieltjes transformation

1988 ◽  
Vol 110 (1-2) ◽  
pp. 73-78 ◽  
Author(s):  
Gordon Sinnamon
Keyword(s):  
Double Series ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Lebesgue Spaces ◽  
Weighted Lebesgue Spaces ◽  
Necessary And Sufficient

SynopsisA necessary and sufficient condition for the boundedness of the generalised Stieltjes transformation on weighted Lebesgue spaces is obtained and applied to extend the Hilbert double series theorem.

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.

The maximal operator on weighted variable Lebesgue spaces

2011 ◽  
Vol 14 (3) ◽  
Author(s):  
David Cruz-Uribe ◽  
Lars Diening ◽  
Peter Hästö
Keyword(s):  
Maximal Operator ◽  
Variable Exponent ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Lebesgue Spaces ◽  
Hölder Continuous ◽  
Variable Lebesgue Spaces ◽  
Muckenhoupt Condition ◽  
Necessary And Sufficient ◽  
Weighted Variable

AbstractWe study the boundedness of the maximal operator on the weighted variable exponent Lebesgue spaces L ωp(·) (Ω). For a given log-Hölder continuous exponent p with 1 < inf p ⩽ supp < ∞ we present a necessary and sufficient condition on the weight ω for the boundedness of M. This condition is a generalization of the classical Muckenhoupt condition.

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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