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.

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.

A Characterization of Bergman Spaces on the Unit Ball of ℂn. II

2012 ◽  
Vol 55 (1) ◽  
pp. 146-152 ◽  
Author(s):  
Songxiao Li ◽  
Hasi Wulan ◽  
Kehe Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Double Integrals

AbstractIt has been shown that a holomorphic function f in the unit ball of ℂn belongs to the weighted Bergman space , p > n + 1 + α, if and only if the function | f(z) – f(w)|/|1 – 〈z, w〉| is in Lp( × , dvβ × dvβ), where β = (p + α – n – 1)/2 and dvβ(z) = (1 – |z|2)βdv(z). In this paper we consider the range 0 < p < n + 1 + α and show that in this case, f ∈ (i) if and only if the function | f(z) – f(w)|/|1 – hz, wi| is in Lp( × , dvα × dvα), (ii) if and only if the function | f(z)– f(w)|/|z–w| is in Lp( × , dvα × dvα). We think the revealed difference in the weights for the double integrals between the cases 0 < p < n + 1 + α and p > n + 1 + α is particularly interesting.

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

On Density Conditions for Interpolation in the Ball

2003 ◽  
Vol 46 (4) ◽  
pp. 559-574 ◽  
Author(s):  
Nicolas Marco ◽  
Xavier Massaneda
Keyword(s):  
Unit Ball ◽  
Polynomial Growth ◽  
Entire Functions ◽  
Holomorphic Functions ◽  
Weighted Bergman Space ◽  
Sufficient Condition ◽  
Density Condition ◽  
Interpolating Sequences ◽  
Class A ◽  
Spaces Of Holomorphic Functions

AbstractIn this paper we study interpolating sequences for two related spaces of holomorphic functions in the unit ball of Cn, n > 1. We first give density conditions for a sequence to be interpolating for the class A−∞ of holomorphic functions with polynomial growth. The sufficient condition is formally identical to the characterizing condition in dimension 1, whereas the necessary one goes along the lines of the results given by Li and Taylor for some spaces of entire functions. In the second part of the paper we show that a density condition, which for n = 1 coincides with the characterizing condition given by Seip, is sufficient for interpolation in the (weighted) Bergman space.

scholarly journals Volterra composition operators from generalized weighted weighted Bergman spaces toµ-Bloch spaces

2009 ◽  
Vol 7 (3) ◽  
pp. 225-240 ◽  
Author(s):  
Xiangling Zhu
Keyword(s):  
Holomorphic Function ◽  
Unit Ball ◽  
Bergman Space ◽  
Composition Operators ◽  
Bloch Space ◽  
Bergman Spaces ◽  
Weighted Bergman Space ◽  
Weighted Bergman Spaces ◽  
Bloch Spaces

Letφbe a holomorphic self-map andgbe a fixed holomorphic function on the unit ballB. The boundedness and compactness of the operatorTg,φf(z)=∫01f(φ(tz))ℜg(tz)dttfrom the generalized weighted Bergman space into the µ-Bloch space are studied in this paper.

scholarly journals Multiplication Operator with BMO Symbols and Berezin Transform

2015 ◽  
Vol 2015 ◽  
pp. 1-4
Author(s):  
Xue Feng ◽  
Kan Zhang ◽  
Jianguo Dong ◽  
Xianmin Liu ◽  
Chi Guan
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Sufficient Conditions ◽  
Multiplication Operator ◽  
Berezin Transform ◽  
Weighted Bergman Space ◽  
Necessary And Sufficient Conditions ◽  
Special Symbol ◽  
Necessary And Sufficient

We discuss multiplication operator with a special symbol on the weighted Bergman space of the unit ball. We give the necessary and sufficient conditions for the compactness of multiplication operator on the weighted Bergman space of the unit ball.

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