Essential norms of weighted composition operators from weighted Bergman space to mixed-norm space on the unit ball

2012 ◽  
Vol 29 (3) ◽  
pp. 547-556 ◽  
Author(s):  
Ze Hua Zhou ◽  
Yu Xia Liang ◽  
Hong Gang Zeng
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Composition Operators ◽  
Weighted Bergman Space ◽  
Mixed Norm ◽  
Weighted Composition Operators ◽  
Mixed Norm Space ◽  
Norm Space ◽  
Weighted Composition

scholarly journals Weighted Iterated Radial Composition Operators between Some Spaces of Holomorphic Functions on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-14 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Composition Operators ◽  
Holomorphic Functions ◽  
Mixed Norm ◽  
Mixed Norm Space ◽  
Type Space ◽  
Spaces Of Holomorphic Functions ◽  
Schmidt Norm ◽  
Norm Space ◽  
Weighted Type

The boundedness and compactness of weighted iterated radial composition operators from the mixed-norm space to the weighted-type space and the little weighted-type space on the unit ball are characterized here. We also calculate the Hilbert-Schmidt norm of the operator on the weighted Bergman-Hilbert space as well as on the Hardy space.

GENERALISED WEIGHTED COMPOSITION OPERATORS ON BERGMAN SPACES INDUCED BY DOUBLING WEIGHTS

2021 ◽  
pp. 1-13
Author(s):  
BIN LIU
Keyword(s):  
Bergman Space ◽  
Lebesgue Space ◽  
Borel Measure ◽  
Composition Operators ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Weighted Composition Operators ◽  
Doubling Weights ◽  
Weighted Composition

Abstract We characterise bounded and compact generalised weighted composition operators acting from the weighted Bergman space $A^p_\omega $ , where $0<p<\infty $ and $\omega $ belongs to the class $\mathcal {D}$ of radial weights satisfying a two-sided doubling condition, to a Lebesgue space $L^q_\nu $ . On the way, we establish a new embedding theorem on weighted Bergman spaces $A^p_\omega $ which generalises the well-known characterisation of the boundedness of the differentiation operator $D^n(f)=f^{(n)}$ from the classical weighted Bergman space $A^p_\alpha $ to the Lebesgue space $L^q_\mu $ , induced by a positive Borel measure $\mu $ , to the setting of doubling weights.

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.

scholarly journals Compact differences of weighted composition operators

2020 ◽  
Author(s):  
Bin Liu ◽  
Jouni Rättyä
Keyword(s):  
Bergman Space ◽  
Composition Operators ◽  
Weighted Bergman Space ◽  
Carleson Measures ◽  
Weighted Composition Operators ◽  
Doubling Weights ◽  
Weighted Composition ◽  
The Way

AbstractCompact differences of two weighted composition operators acting from the weighted Bergman space $$A^p_{\omega }$$ A ω p to another weighted Bergman space $$A^q_{\nu }$$ A ν q , where $$0<p\le q<\infty $$ 0 < p ≤ q < ∞ and $$\omega ,\nu $$ ω , ν belong to the class $${\mathcal {D}}$$ D of radial weights satisfying two-sided doubling conditions, are characterized. On the way to the proof a new description of q-Carleson measures for $$A^p_{\omega }$$ A ω p , with $$\omega \in {\mathcal {D}}$$ ω ∈ D , in terms of pseudohyperbolic discs is established. This last-mentioned result generalizes the well-known characterization of q-Carleson measures for the classical weighted Bergman space $$A^p_{\alpha }$$ A α p with $$-1<\alpha <\infty $$ - 1 < α < ∞ to the setting of doubling weights.

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