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.

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 .

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