UNIFORMLY BOUNDED COMPOSITION OPERATORS

2015 ◽  
Vol 92 (3) ◽  
pp. 463-469
Author(s):  
DOROTA GŁAZOWSKA ◽  
JANUSZ MATKOWSKI
Keyword(s):  
Weight Function ◽  
Composition Operators ◽  
Function Variable ◽  
Nemytskij Operator ◽  
Uniformly Bounded

We prove that if a uniformly bounded (or equidistantly uniformly bounded) Nemytskij operator maps the space of functions of bounded ${\it\varphi}$-variation with weight function in the sense of Riesz into another space of that type (with the same weight function) and its generator is continuous with respect to the second variable, then this generator is affine in the function variable (traditionally, in the second variable).

scholarly journals UNIFORMLY BOUNDED COMPOSITION OPERATORS ON A BANACH SPACE OF BOUNDED WIENER-YOUNG VARIATION FUNCTIONS

2013 ◽  
Vol 50 (2) ◽  
pp. 675-685 ◽  
Author(s):  
Dorota Glazowska ◽  
Jose Atilio Guerrero ◽  
Janusz Matkowski ◽  
Nelson Merentes
Keyword(s):  
Banach Space ◽  
Composition Operators ◽  
Uniformly Bounded

Uniformly bounded composition operators in the banach space of bounded (p, k)-variation in the sense of Riesz-Popoviciu

2013 ◽  
Vol 11 (2) ◽  
Author(s):  
Francy Armao ◽  
Dorota Głazowska ◽  
Sergio Rivas ◽  
Jessica Rojas
Keyword(s):  
Banach Space ◽  
Composition Operator ◽  
Composition Operators ◽  
Uniformly Bounded

AbstractWe prove that if the composition operator F generated by a function f: [a, b] × ℝ → ℝ maps the space of bounded (p, k)-variation in the sense of Riesz-Popoviciu, p ≥ 1, k an integer, denoted by RV(p,k)[a, b], into itself and is uniformly bounded then RV(p,k)[a, b] satisfies the Matkowski condition.

The form of locally defined operators in waterman spaces

2021 ◽  
Vol 71 (6) ◽  
pp. 1529-1544
Author(s):  
Małgorzata Wróbel
Keyword(s):  
Banach Spaces ◽  
Bounded Variation ◽  
Composition Operators ◽  
Representation Formula ◽  
Continuous Functions ◽  
Functions Of Bounded Variation ◽  
Spaces Of Continuous Functions ◽  
Local Operators ◽  
Uniformly Bounded

Abstract A representation formula for locally defined operators acting between Banach spaces of continuous functions of bounded variation in the Waterman sense is presented. Moreover, the Nemytskij composition operators will be investigated and some consequences for locally bounded as well as uniformly bounded local operators will be given.

Uniformly bounded composition operators in the Banach space of absolutely continuous functions

2012 ◽  
Vol 75 (13) ◽  
pp. 4995-5001 ◽  
Author(s):  
D. Głazowska ◽  
J. Matkowski ◽  
N. Merentes ◽  
J.L. Sánchez Hernández
Keyword(s):  
Banach Space ◽  
Composition Operators ◽  
Continuous Functions ◽  
Absolutely Continuous Functions ◽  
Absolutely Continuous ◽  
Uniformly Bounded

scholarly journals A New Essential Norm Estimate of Composition Operators from Weighted Bloch Space into -Bloch Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
René E. Castillo ◽  
Julio C. Ramos-Fernández ◽  
Edixon M. Rojas
Keyword(s):  
Weight Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Special Function ◽  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces ◽  
Norm Estimate ◽  
Operator Mapping

Let be any weight function defined on the unit disk and let be an analytic self-map of . In the present paper, we show that the essential norm of composition operator mapping from the weighted Bloch space to -Bloch space is comparable to where for ,   is a certain special function in the weighted Bloch space. As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003).

A NEW ESSENTIAL NORM ESTIMATE OF COMPOSITION OPERATORS FROM α-BLOCH SPACES INTO μ-BLOCH SPACES

2013 ◽  
Vol 24 (14) ◽  
pp. 1350104 ◽  
Author(s):  
JULIO C. RAMOS-FERNÁNDEZ
Keyword(s):  
Weight Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Besov Spaces ◽  
Special Function ◽  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces ◽  
Norm Estimate

Let μ be any weight function defined on the unit disk 𝔻 and let ϕ be an analytic self-map of 𝔻. In this paper, we show that the essential norm of composition operator Cϕ mapping from the α-Bloch space, with α > 0, to μ-Bloch space [Formula: see text] is comparable to [Formula: see text] where, for a ∈ 𝔻, σa is a certain special function in α-Bloch space. As a consequence of our estimate, we extend recent results, about the compactness of composition operators, due to Tjani in [Compact composition operators on Besov spaces, Trans. Amer. Math. Soc.355(11) (2003) 4683–4698] and Malavé Ramírez and Ramos-Fernández in [On a criterion for continuity and compactness of composition operators acting on α-Bloch spaces, C. R. Math. Acad. Sci. Paris351 (2013) 23–26, http://dx.doi.org/10.1016/j.crma.2012.11.013 ].

scholarly journals Uniformly bounded set-valued composition operators in the spaces of functions of bounded variation in the sense of Wiener

2015 ◽  
Vol 14 (4) ◽  
pp. 41-51
Author(s):  
José Atilio Guerrero ◽  
◽  
Janusz Matkowski ◽  
Nelson Merentes ◽  
Małgorzata Wróbel ◽  
...  
Keyword(s):  
Bounded Variation ◽  
Composition Operators ◽  
Functions Of Bounded Variation ◽  
Bounded Set ◽  
Uniformly Bounded

scholarly journals Upper and Lower Bounds for Essential Norm of Weighted Composition Operators from Bergman Spaces with Békollé Weights

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Elina Subhadarsini ◽  
Ajay K. Sharma
Keyword(s):  
Weight Function ◽  
Lower Bounds ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Bergman Spaces ◽  
Essential Norm ◽  
Normal Weight ◽  
Upper And Lower Bounds ◽  
Weighted Bergman Spaces ◽  
Weighted Composition

Let σ be a weight function such that σ / 1 − z 2 α is in the class B p 0 α of Békollé weights, μ a normal weight function, ψ a holomorphic map on D , and φ a holomorphic self-map on D . In this paper, we give upper and lower bounds for essential norm of weighted composition operator W ψ , φ acting from weighted Bergman spaces A p σ to Bloch-type spaces B μ .

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