Product-Type Operators from the Bloch Space into Zygmund-Type Spaces

2021 ◽  
Author(s):  
Ebrahim Abbasi ◽  
Xiangling Zhu
Keyword(s):  
Bloch Space ◽  
Product Type ◽  
Type Spaces

scholarly journals Multiplicative Isometries and Isometric Zero-Divisors

2010 ◽  
Vol 62 (5) ◽  
pp. 961-974 ◽  
Author(s):  
Alexandru Aleman ◽  
Peter Duren ◽  
María J. Martín ◽  
Dragan Vukotić
Keyword(s):  
Banach Spaces ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Spaces ◽  
Zero Divisors ◽  
Pointwise Multipliers ◽  
Type Spaces ◽  
Dirichlet Type Spaces ◽  
Coefficient Multipliers ◽  
Spaces Of Analytic Functions

AbstractFor some Banach spaces of analytic functions in the unit disk (weighted Bergman spaces, Bloch space, Dirichlet-type spaces), the isometric pointwise multipliers are found to be unimodular constants. As a consequence, it is shown that none of those spaces have isometric zero-divisors. Isometric coefficient multipliers are also investigated.

scholarly journals Extended Cesáro operators between generalized Besov spaces and Bloch type spaces in the unit ball

2009 ◽  
Vol 7 (3) ◽  
pp. 209-223 ◽  
Author(s):  
Ze-Hua Zhou ◽  
Min Zhu
Keyword(s):  
Unit Ball ◽  
Besov Space ◽  
Besov Spaces ◽  
Complex Space ◽  
Bloch Space ◽  
Sufficient Conditions ◽  
Cesàro Operator ◽  
Type Spaces ◽  
Necessary And Sufficient ◽  
Cesaro Operator

Let 𝑔 be a holomorphic of the unit ballBin then-dimensional complex space, and denote byTgthe extended Cesáro operator with symbolg. Let 0 <p< +∞, −n− 1 <q< +∞,q> −1 and α > 0, starting with a brief introduction to well known results about Cesáro operator, we investigate the boundedness and compactness ofTgbetween generalized Besov spaceB(p, q)and 𝛼α- Bloch spaceℬαin the unit ball, and also present some necessary and sufficient conditions.

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].

scholarly journals Weighted Differentiation Composition Operators to Bloch-Type Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Junming Liu ◽  
Zengjian Lou ◽  
Ajay K. Sharma
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Type Spaces

We characterized the boundedness and compactness of weighted differentiation composition operators from BMOA and the Bloch space to Bloch-type spaces. Moreover, we obtain new characterizations of boundedness and compactness of weighted differentiation composition operators.

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