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.

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 Distance of a Bloch Function to the Little Bloch Space

2006 ◽  
Vol 74 (1) ◽  
pp. 101-119 ◽  
Author(s):  
Maria Tjani
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Function ◽  
Type Spaces ◽  
Little Bloch Space ◽  
Equivalent Expressions

Motivated by a formula of P. Jones that gives the distance of a Bloch function to BMOA, the space of bounded mean oscillations, we obtain several formulas for the distance of a Bloch function to the little Bloch space, β0. Immediate consequences are equivalent expressions for functions in β0. We also give several examples of distances of specific functions to β0. We comment on connections between distance to β0 and the essential norm of some composition operators on the Bloch space, β. Finally we show that the distance formulas in β have Bloch type spaces analogues.

Univalently Induced, Closed Range, Composition Operators on the Bloch-type Spaces

2012 ◽  
Vol 55 (2) ◽  
pp. 441-448 ◽  
Author(s):  
Nina Zorboska
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Closed Range ◽  
Type Spaces

AbstractWhile there is a large variety of univalently induced closed range composition operators on the Bloch space, we show that the only univalently induced, closed range, composition operators on the Bloch-type spaces Bα with α ≠ 1 are the ones induced by a disc automorphism.

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