Generalized Composition Operators from the Lipschitz Space into the Zygmund Space

2020 ◽  
Vol 55 (5) ◽  
pp. 283-290
Author(s):  
S. Mahmoudfakheh ◽  
H. Vaezi
Keyword(s):  
Composition Operators ◽  
Lipschitz Space ◽  
Zygmund Space

scholarly journals Composition Operators on Some Banach Spaces of Harmonic Mappings

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Munirah Aljuaid ◽  
Flavia Colonna
Keyword(s):  
Banach Spaces ◽  
Unit Disk ◽  
Besov Spaces ◽  
Analytic Functions ◽  
Composition Operators ◽  
Harmonic Mappings ◽  
Open Unit ◽  
Open Unit Disk ◽  
Zygmund Space ◽  
Spaces Of Analytic Functions

We study the composition operators on Banach spaces of harmonic mappings that extend several well-known Banach spaces of analytic functions on the open unit disk in the complex plane, including the α-Bloch spaces, the growth spaces, the Zygmund space, the analytic Besov spaces, and the space BMOA.

scholarly journals Weighted Composition Operators from the Bloch Space and the Analytic Besov Spaces into the Zygmund Space

2013 ◽  
Vol 2013 ◽  
pp. 1-9 ◽  
Author(s):  
Flavia Colonna ◽  
Songxiao Li
Keyword(s):  
Composition Operator ◽  
Besov Spaces ◽  
Composition Operators ◽  
Bloch Space ◽  
Weighted Composition Operators ◽  
Zygmund Space ◽  
Weighted Composition ◽  
Special Case

We provide several characterizations of the bounded and the compact weighted composition operators from the Bloch space and the analytic Besov spaces (with ) into the Zygmund space . As a special case, we show that the bounded (resp., compact) composition operators from , , and to coincide. In addition, the boundedness and the compactness of the composition operator can be characterized in terms of the boundedness (resp., convergence to 0, under the boundedness assumption of the operator) of the Zygmund norm of the powers of the symbol.

Composition Operators on the Lipschitz Space of a Tree

2013 ◽  
Vol 11 (1) ◽  
pp. 97-108 ◽  
Author(s):  
Robert F. Allen ◽  
Flavia Colonna ◽  
Glenn R. Easley
Keyword(s):  
Composition Operators ◽  
Lipschitz Space

scholarly journals Essential norm of weighted composition operators from the Bloch space and the Zygmund space to the Bloch space

Filomat ◽  
2018 ◽  
Vol 32 (2) ◽  
pp. 681-691 ◽  
Author(s):  
Qinghua Hu ◽  
Songxiao Li
Keyword(s):  
Composition Operators ◽  
Bloch Space ◽  
Essential Norm ◽  
Weighted Composition Operators ◽  
Zygmund Space ◽  
Weighted Composition

In this paper, we give some estimates for the essential norm of weighted composition operators from the Bloch space and the Zygmund space to the Bloch space.

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