scholarly journals On a New Integral-Type Operator from the Weighted Bergman Space to the Bloch-Type Space on the Unit Ball

2008 ◽  
Vol 2008 ◽  
pp. 1-14 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Weighted Bergman Space ◽  
Type Operator ◽  
Upper And Lower Bounds ◽  
Integral Type ◽  
Type Space ◽  
Bloch Type Space

We introduce an integral-type operator, denoted byPφg, on the space of holomorphic functions on the unit ballB⊂ℂn, which is an extension of the product of composition and integral operators on the unit disk. The operator norm ofPφgfrom the weighted Bergman spaceAαp(B)to the Bloch-type spaceℬμ(B)or the little Bloch-type spaceℬμ,0(B)is calculated. The compactness of the operator is characterized in terms of inducing functionsgandφ. Upper and lower bounds for the essential norm of the operatorPφg:Aαp(B)→ℬμ(B), whenp>1, are also given.

scholarly journals Norm and Essential Norm of an Integral-Type Operator from the Dirichlet Space to the Bloch-Type Space on the Unit Ball

2010 ◽  
Vol 2010 ◽  
pp. 1-9 ◽  
Author(s):  
Stevo Stević
Keyword(s):  
Unit Ball ◽  
Dirichlet Space ◽  
Essential Norm ◽  
Operator Norm ◽  
Type Operator ◽  
Integral Type ◽  
Type Space ◽  
Bloch Type Space

Operator norm and essential norm of an integral-type operator, recently introduced by this author, from the Dirichlet space to the Bloch-type space on the unit ball in are calculated here.

scholarly journals ESSENTIAL NORM OF EXTENDED CESÀRO OPERATORS FROM ONE BERGMAN SPACE TO ANOTHER

2011 ◽  
Vol 85 (2) ◽  
pp. 307-314 ◽  
Author(s):  
ZHANGJIAN HU
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Holomorphic Functions ◽  
Essential Norm ◽  
Normal Weight ◽  
Cesàro Operator ◽  
Radial Derivative ◽  
Image Position ◽  
Cesaro Operator

AbstractLet Ap(φ) be the pth Bergman space consisting of all holomorphic functions f on the unit ball B of ℂn for which $\|f\|^p_{p,\varphi }= \int _B |f(z)|^p \varphi (z) \,dA(z)\lt +\infty $, where φ is a given normal weight. Let Tg be the extended Cesàro operator with holomorphic symbol g. The essential norm of Tg as an operator from Ap (φ) to Aq (φ) is denoted by $\|T_g\|_{e, A^p (\varphi )\to A^q (\varphi )} $. In this paper it is proved that, for p≤q, with 1/k=(1/p)−(1/q) , where ℜg(z) is the radial derivative of g; and for p>q, with 1/s=(1/q)−(1/p) .

The composition type operator on the weighted Bergman space in the unit ball

2015 ◽  
Vol 45 (2) ◽  
pp. 141-150
Author(s):  
Ying GUAN ◽  
Min LI ◽  
XueJun ZHANG ◽  
JianBin XIAO
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Weighted Bergman Space ◽  
Type Operator

scholarly journals On the dual space of a weighted Bergman space on the unit ball ofCn

1988 ◽  
Vol 11 (3) ◽  
pp. 457-464 ◽  
Author(s):  
J. S. Choa ◽  
H. O. Kim
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Dual Space ◽  
Holomorphic Functions ◽  
Weighted Bergman Space ◽  
Mackey Topology

The weighted Bergman spaceAαp(Bn)(0<p<1), of the holomorphic functions on the unit ballBnofCnforms anF-space. We find the dual space ofAαp(Bn)by determining its Mackey topology.

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