Weighted composition followed by differentiation between weighted Bergman space and (H^\infty) on the unit ball

2015 ◽  
Vol 9 ◽  
pp. 169-176
Author(s):  
Chao Zhang ◽  
Sui Huang
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Weighted Bergman Space ◽  
Weighted Composition

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.

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 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.

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 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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