scholarly journals Inequalities Involving Essential Norm Estimates of Product-Type Operators

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Manisha Devi ◽  
Ajay K. Sharma ◽  
Kuldip Raj
Keyword(s):  
Analytic Function ◽  
Holomorphic Function ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Open Unit ◽  
Open Unit Disk ◽  
Norm Estimates ◽  
Type Spaces ◽  
Weighted Composition ◽  
Dirichlet Type Spaces

Consider an open unit disk D = z ∈ ℂ : z < 1 in the complex plane ℂ , ξ a holomorphic function on D , and ψ a holomorphic self-map of D . For an analytic function f , the weighted composition operator is denoted and defined as follows: W ξ , ψ f z = ξ z f ψ z . We estimate the essential norm of this operator from Dirichlet-type spaces to Bers-type spaces and Bloch-type spaces.

scholarly journals Essential norm of weighted composition operator betweenα-Bloch space andβ-Bloch space in polydiscs

2004 ◽  
Vol 2004 (71) ◽  
pp. 3941-3950
Author(s):  
Li Songxiao ◽  
Zhu Xiangling
Keyword(s):  
Holomorphic Function ◽  
Composition Operator ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Weighted Composition

Letφ(z)=(φ1(z),…,φn(z))be a holomorphic self-map of&#x1D53B;nandψ(z)a holomorphic function on&#x1D53B;n, where&#x1D53B;nis the unit polydiscs ofℂn. Let0<α,β<1, we compute the essential norm of a weighted composition operatorψCφbetweenα-Bloch spaceℬα(&#x1D53B;n)andβ-Bloch spaceℬβ(&#x1D53B;n).

scholarly journals Weighted Composition Operators from Hardy Spaces into Logarithmic Bloch Spaces

2012 ◽  
Vol 2012 ◽  
pp. 1-20 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Banach Space ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Weighted Composition

The logarithmic Bloch spaceBlog⁡is the Banach space of analytic functions on the open unit disk&#x1D53B;whose elementsfsatisfy the condition∥f∥=sup⁡z∈&#x1D53B;(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|<∞. In this work we characterize the bounded and the compact weighted composition operators from the Hardy spaceHp(with1≤p≤∞) into the logarithmic Bloch space. We also provide boundedness and compactness criteria for the weighted composition operator mappingHpinto the little logarithmic Bloch space defined as the subspace ofBlog⁡consisting of the functionsfsuch thatlim⁡|z|→1(1-|z|2)log⁡  (2/(1-|z|2))|f'(z)|=0.

scholarly journals Riemann-Stieltjes operators between Bergman-type spaces andα-Bloch spaces

2006 ◽  
Vol 2006 ◽  
pp. 1-17 ◽  
Author(s):  
Songxiao Li
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Complex Plane ◽  
Integral Operators ◽  
Open Unit ◽  
Open Unit Disk ◽  
Bloch Spaces ◽  
Type Spaces

We study the following integral operators:Jgf(z)=∫0zf(ξ)g′(ξ)dξ;Igf(z)=∫0zf′(ξ)g(ξ)dξ, wheregis an analytic function on the open unit disk in the complex plane. The boundedness and compactness ofJg,Igbetween the Bergman-type spaces and theα-Bloch spaces are investigated.

scholarly journals WEIGHTED COMPOSITION OPERATORS FROM F(p, q, s) TO BLOCH TYPE SPACES ON THE UNIT BALL

2008 ◽  
Vol 19 (08) ◽  
pp. 899-926 ◽  
Author(s):  
ZE-HUA ZHOU ◽  
REN-YU CHEN
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Composition Operator ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Weighted Composition Operators ◽  
Type Spaces ◽  
Weighted Composition

Let ϕ(z) = (ϕ1(z),…,ϕn(z)) be a holomorphic self-map of B and ψ(z) a holomorphic function on B, where B is the unit ball of ℂn. Let 0 < p, s < +∞, -n - 1 < q < +∞, q+s > -1 and α ≥ 0, this paper characterizes boundedness and compactness of weighted composition operator Wψ,ϕ induced by ϕ and ψ between the space F(p, q, s) and α-Bloch space [Formula: see text].

Boundary vs. interior conditions associated with weighted composition operators

2014 ◽  
Vol 12 (5) ◽  
Author(s):  
Kei Izuchi ◽  
Yuko Izuchi ◽  
Shûichi Ohno
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Essential Norm ◽  
Weight Functions ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Weighted Composition ◽  
The Difference ◽  
Harmonic And Analytic Functions

AbstractAssociated with some properties of weighted composition operators on the spaces of bounded harmonic and analytic functions on the open unit disk $$\mathbb{D}$$, we obtain conditions in terms of behavior of weight functions and analytic self-maps on the interior $$\mathbb{D}$$ and on the boundary $$\partial \mathbb{D}$$ respectively. We give direct proofs of the equivalence of these interior and boundary conditions. Furthermore we give another proof of the estimate for the essential norm of the difference of weighted composition operators.

scholarly journals ORDER BOUNDED WEIGHTED COMPOSITION OPERATORS

2012 ◽  
Vol 93 (3) ◽  
pp. 333-343
Author(s):  
ELKE WOLF
Keyword(s):  
Composition Operators ◽  
Weighted Composition Operator ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Weighted Composition ◽  
Weighted Banach Spaces ◽  
Analytic Maps

AbstractLet $\phi $ and $\psi $ be analytic maps on the open unit disk $D$ such that $\phi (D) \subset D$. Such maps induce a weighted composition operator $C_{\phi ,\psi }$ acting on weighted Banach spaces of type $H^{\infty }$or on weighted Bergman spaces, respectively. We study when such operators are order bounded.

scholarly journals Weighted composition operators in weighted Banach spaces of analytic functions

2000 ◽  
Vol 69 (1) ◽  
pp. 41-60 ◽  
Author(s):  
M. D. Contreras ◽  
A. G. Hernandez-Diaz
Keyword(s):  
Banach Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Type Spaces ◽  
Weighted Composition ◽  
Weighted Banach Spaces ◽  
Spaces Of Analytic Functions

AbstractWe characterize the boundedness and compactness of weighted composition operators between weighted Banach spaces of analytic functions and . we estimate the essential norm of a weighted composition operator and compute it for those Banach spaces which are isomorphic to c0. We also show that, when such an operator is not compact, it is an isomorphism on a subspace isomorphic to c0 or l∞. Finally, we apply these results to study composition operators between Bloch type spaces and little Bloch type spaces.

Essential norms of weighted differentiation composition operators between Zygmund type spaces and Bloch type spaces

Filomat ◽  
2017 ◽  
Vol 31 (9) ◽  
pp. 2877-2889 ◽  
Author(s):  
Amir Sanatpour ◽  
Mostafa Hassanlou
Keyword(s):  
Composition Operators ◽  
Sufficient Conditions ◽  
Essential Norm ◽  
Necessary And Sufficient Conditions ◽  
Norm Estimates ◽  
Type Spaces ◽  
Necessary And Sufficient

We study boundedness of weighted differentiation composition operators Dk?,u between Zygmund type spaces Z? and Bloch type spaces ?. We also give essential norm estimates of such operators in different cases of k ? N and 0 < ?,? < ?. Applying our essential norm estimates, we get necessary and sufficient conditions for the compactness of these operators.

scholarly journals On the Fekete-Szegö problem

2000 ◽  
Vol 24 (9) ◽  
pp. 577-581 ◽  
Author(s):  
B. A. Frasin ◽  
Maslina Darus
Keyword(s):  
Analytic Function ◽  
Unit Disk ◽  
Upper Bound ◽  
Starlike Functions ◽  
Open Unit ◽  
Open Unit Disk ◽  
Strongly Starlike Functions ◽  
Strongly Starlike

Letf(z)=z+a2z2+a3z3+⋯be an analytic function in the open unit disk. A sharp upper bound is obtained for|a3−μa22|by using the classes of strongly starlike functions of orderβand typeαwhenμ≥1.

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