Composition operator between normal weight Dirichlet type space and Bloch type space

2021 ◽  
pp. 1-14
Author(s):  
Xuejun Zhang ◽  
Ying Huang
Keyword(s):  
Composition Operator ◽  
Normal Weight ◽  
Type Space ◽  
Bloch Type Space ◽  
Dirichlet Type ◽  
Dirichlet Type Space

scholarly journals The essential norm of a composition operator mapping intoQktype spaces

2008 ◽  
Vol 6 (3) ◽  
pp. 241-258 ◽  
Author(s):  
Marko Kotilainen ◽  
Jouni Rättyä
Keyword(s):  
Asymptotic Formula ◽  
Composition Operator ◽  
Unit Disc ◽  
Bloch Space ◽  
Integral Condition ◽  
Essential Norm ◽  
Type Space ◽  
Operator Mapping ◽  
Dirichlet Type ◽  
Dirichlet Type Space

An asymptotic formula for the essential norm of the composition operatorCφ(f):=f∘φ, induced by an analytic self-mapφof the unit disc, mapping from theα-Bloch spaceℬαor the Dirichlet type spaceDαpintoQk(p,q)is established in terms of an integral condition.

scholarly journals Toeplitz Operators on Dirichlet-Type Space of Unit Ball

2014 ◽  
Vol 2014 ◽  
pp. 1-13
Author(s):  
Jin Xia ◽  
Xiaofeng Wang ◽  
Guangfu Cao
Keyword(s):  
Toeplitz Operator ◽  
Boundary Point ◽  
Toeplitz Operators ◽  
Radial Function ◽  
Type Space ◽  
Dirichlet Type ◽  
Algebraic Properties ◽  
Commuting Problem ◽  
Product Problem ◽  
Dirichlet Type Space

We construct a functionuinL2Bn, dVwhich is unbounded on any neighborhood of each boundary point ofBnsuch that Toeplitz operatorTuis a Schattenp-class0<p<∞operator on Dirichlet-type spaceDBn, dV. Then, we discuss some algebraic properties of Toeplitz operators with radial symbols on the Dirichlet-type spaceDBn, dV. We determine when the product of two Toeplitz operators with radial symbols is a Toeplitz operator. We investigate the zero-product problem for several Toeplitz operators with radial symbols. Furthermore, the corresponding commuting problem of Toeplitz operators whose symbols are of the formξkuis studied, wherek ∈ Zn,ξ ∈ ∂Bn, anduis a radial function.

scholarly journals Weighted composition operators from Bloch-type into Bers-type spaces

2021 ◽  
Vol 29 (2) ◽  
pp. 243-250
Author(s):  
HAMID VAEZI ◽  
MOHAMAD NAGHLISAR
Keyword(s):  
Composition Operator ◽  
Composition Operators ◽  
Weighted Composition Operator ◽  
Sufficient Conditions ◽  
Weighted Composition Operators ◽  
Type Space ◽  
Bloch Type Space ◽  
Type Spaces ◽  
Weighted Composition ◽  
Necessary And Sufficient

In this paper we consider the weighted composition operator uC_{\varphi} from Bloch-type space B^{\alpha} into Bers-type space H_{\beta}^{\infty}, in three cases, \alpha>1, \alpha=1 and \alpha<1. We give the necessary and sufficient conditions for boundedness and compactness of the above operator.

scholarly journals Characterizations of a Class of Dirichlet-Type Spaces and Related Operators

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Xiaosong Liu ◽  
Songxiao Li
Keyword(s):  
Boundary Value ◽  
Type Space ◽  
Dirichlet Type ◽  
Type Spaces ◽  
Dirichlet Type Spaces ◽  
Dirichlet Type Space

In this paper, some characterizations are given in terms of the boundary value and Poisson extension for the Dirichlet-type space D μ . The multipliers of D μ and Hankel-type operators from D μ to L 2 P μ d A are also investigated.

scholarly journals Weighted Composition Operator from Mixed Norm Space to Bloch-Type Space on the Unit Ball

2014 ◽  
Vol 2014 ◽  
pp. 1-10
Author(s):  
Yu-Xia Liang ◽  
Ren-Yu Chen
Keyword(s):  
Unit Ball ◽  
Composition Operator ◽  
Weighted Composition Operator ◽  
Mixed Norm ◽  
Mixed Norm Space ◽  
Type Space ◽  
Bloch Type Space ◽  
Norm Space ◽  
Weighted Composition

We discuss the boundedness and compactness of the weighted composition operator from mixed norm space to Bloch-type space on the unit ball ofCn.

Characterizations of the Dirichlet-Type Space

2014 ◽  
Vol 9 (6) ◽  
pp. 1269-1286 ◽  
Author(s):  
Xiaosong Liu ◽  
Gerardo R. Chacón ◽  
Zengjian Lou
Keyword(s):  
Type Space ◽  
Dirichlet Type ◽  
Dirichlet Type Space

scholarly journals Composition operators from Bloch type spaces to F(p, q, s) spaces

Filomat ◽  
2007 ◽  
Vol 21 (2) ◽  
pp. 11-20 ◽  
Author(s):  
Xiangling Zhu
Keyword(s):  
Unit Disk ◽  
Composition Operator ◽  
Composition Operators ◽  
Type Space ◽  
Bloch Type Space ◽  
Type Spaces

Suppose that if is an analytic self-map of the unit disk, the compactness of the composition operator C? from the Bloch type space into the space F(p, q, s) is investigated .

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