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 A New Essential Norm Estimate of Composition Operators from Weighted Bloch Space into -Bloch Spaces

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
René E. Castillo ◽  
Julio C. Ramos-Fernández ◽  
Edixon M. Rojas
Keyword(s):  
Weight Function ◽  
Unit Disk ◽  
Composition Operator ◽  
Special Function ◽  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Bloch Spaces ◽  
Norm Estimate ◽  
Operator Mapping

Let be any weight function defined on the unit disk and let be an analytic self-map of . In the present paper, we show that the essential norm of composition operator mapping from the weighted Bloch space to -Bloch space is comparable to where for ,   is a certain special function in the weighted Bloch space. As a consequence of our estimate, we extend the results about the compactness of composition operators due to Tjani (2003).

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.

The Essential Norm of a Bloch-to-Qp Composition Operator

2004 ◽  
Vol 47 (1) ◽  
pp. 49-59 ◽  
Author(s):  
Mikael Lindstróm ◽  
Shamil Makhmutov ◽  
Jari Taskinen
Keyword(s):  
Composition Operator ◽  
Bloch Space ◽  
Essential Norm

AbstractThe Qp spaces coincide with the Bloch space for p > 1 and are subspaces of BMOA for 0 < p ≤ 1. We obtain lower and upper estimates for the essential norm of a composition operator from the Bloch space into Qp, in particular from the Bloch space into BMOA.

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 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 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.

scholarly journals Weighted differentiation composition operators from the logarithmic Bloch space to the weighted-type space

2016 ◽  
Vol 24 (3) ◽  
pp. 223-240
Author(s):  
Songxiao Li ◽  
Stevo Stević
Keyword(s):  
Asymptotic Estimate ◽  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Type Space ◽  
Weighted Type

AbstractThe boundedness of the weighted differentiation composition opera- tor from the logarithmic Bloch space to the weighted-type space is characterized in terms of the sequence (zn)n∈N0. An asymptotic estimate of the essential norm of the operator is also given in terms of the sequence, which gives a characterization for the compactness of the operator.

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