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 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 SUMS OF WEIGHTED COMPOSITION OPERATORS ON COP

2012 ◽  
Vol 55 (1) ◽  
pp. 229-239 ◽  
Author(s):  
KEI JI IZUCHI ◽  
KOU HEI IZUCHI ◽  
YUKO IZUCHI
Keyword(s):  
Unit Disk ◽  
Composition Operators ◽  
Bloch Space ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disk ◽  
Disk Algebra ◽  
Weighted Composition ◽  
Little Bloch Space

AbstractLet COP =0∩H∞, where0is the little Bloch space on the open unit disk, andA() be the disk algebra on. For non-zero functionsu1,u2,. . .,uN∈A() and distinct analytic self-maps ϕ1,ϕ2,. . .,ϕNsatisfying ϕj∈A() and ∥ϕj∥∞=1 for everyj, it is given characterisations of which the sum of weighted composition operators ∑Nj=1ujCϕjmaps COP intoA().

scholarly journals Non-Weakly Supercyclic Weighted Composition Operators

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Z. Kamali ◽  
K. Hedayatian ◽  
B. Khani Robati
Keyword(s):  
Analytic Functions ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Open Unit ◽  
Weighted Composition Operators ◽  
Open Unit Disc ◽  
Space Of Analytic Functions ◽  
Weighted Composition ◽  
Necessary And Sufficient

We give sufficient conditions under which a weighted composition operator on a Hilbert space of analytic functions is not weakly supercyclic. Also, we give some necessary and sufficient conditions for hypercyclicity and supercyclicity of weighted composition operators on the space of analytic functions on the open unit disc.

scholarly journals Compact Weighted Composition Operators and Multiplication Operators between Hardy Spaces

2008 ◽  
Vol 2008 ◽  
pp. 1-12 ◽  
Author(s):  
Sei-Ichiro Ueki ◽  
Luo Luo
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Hardy Spaces ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Multiplication Operator ◽  
Essential Norm ◽  
Multiplication Operators ◽  
Weighted Composition Operators ◽  
Weighted Composition

We estimate the essential norm of a compact weighted composition operator acting between different Hardy spaces of the unit ball in . Also we will discuss a compact multiplication operator between Hardy spaces.

scholarly journals Characterizations of Bloch-Type Spaces of Harmonic Mappings

2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Munirah Aljuaid ◽  
Flavia Colonna
Keyword(s):  
Banach Space ◽  
Analytic Functions ◽  
Bloch Space ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Space Of Analytic Functions ◽  
Type Spaces ◽  
Growth Space ◽  
Derivatives Of

We study the Banach space BHα (α>0) of the harmonic mappings h on the open unit disk D satisfying the condition supz∈D⁡(1-z2)α(hzz+hz¯z)<∞, where hz and hz¯ denote the first complex partial derivatives of h. We show that several properties that are valid for the space of analytic functions known as the α-Bloch space extend to BHα. In particular, we prove that for α>0 the mappings in BHα can be characterized in terms of a Lipschitz condition relative to the metric defined by dH,α(z,w)=sup⁡{hz-hw:h∈BHα,hBHα≤1}. When α>1, the harmonic α-Bloch space can be viewed as the harmonic growth space of order α-1, while for 0<α<1, BHα is the space of harmonic mappings that are Lipschitz of order 1-α.

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 Essential Norms of Weighted Composition Operators from theα-Bloch Space to a Weighted-Type Space on the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-11 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operator ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Lower And Upper Bounds ◽  
Type Space ◽  
Weighted Composition ◽  
Weighted Type

This paper finds some lower and upper bounds for the essential norm of the weighted composition operator fromα-Bloch spaces to the weighted-type spaceHμ∞on the unit ball for the caseα≥1.

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