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 Extended Cesàro operator between some holomorphic function spaces

2006 ◽  
Vol 74 (3) ◽  
pp. 385-392
Author(s):  
Xiaofen Lv
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Function Spaces ◽  
Mixed Norm ◽  
Cesàro Operator ◽  
Mixed Norm Space ◽  
Type Space ◽  
Bloch Type Space ◽  
Norm Space ◽  
Cesaro Operator

We characterize the boundedness and compactness of the extended Cesàro operator Tg from H∞ to the mixed norm space and Bloch-type space (or little Bloch-type space), where g is a given holomorphic function in the unit ball of Cn and Tg is defined by .

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 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.

scholarly journals ESSENTIAL COMMUTATIVITY OF SOME INTEGRAL AND COMPOSITION OPERATORS

2011 ◽  
Vol 85 (1) ◽  
pp. 143-153
Author(s):  
ZE-HUA ZHOU ◽  
LIANG ZHANG ◽  
HONG-GANG ZENG
Keyword(s):  
Composition Operators ◽  
Integral Operators ◽  
Mixed Norm ◽  
Integral Type ◽  
Mixed Norm Space ◽  
Type Space ◽  
Bloch Type Space ◽  
Norm Space

AbstractIn general, multiplication of operators is not essentially commutative in an algebra generated by integral-type operators and composition operators. In this paper, we characterize the essential commutativity of the integral operators and composition operators from a mixed-norm space to a Bloch-type space, and give a complete description of the universal set of integral operators. Corresponding results for boundedness and compactness are also obtained.

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