M-Besovp-classes and Hankel operators in the Bergman space on the unit ball

1993 ◽  
Vol 61 (4) ◽  
pp. 367-376 ◽  
Author(s):  
Miroljub Jevtić ◽  
Miroslav Pavlović
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Hankel Operators

scholarly journals The Essential Norm of the Generalized Hankel Operators on the Bergman Space of the Unit Ball inCn

2010 ◽  
Vol 2010 ◽  
pp. 1-13 ◽  
Author(s):  
Luo Luo ◽  
Yang Xuemei
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Hankel Operator ◽  
Equivalent Form ◽  
Essential Norm ◽  
Hankel Operators

In 1993, Peloso introduced a kind of operators on the Bergman spaceA2(B)of the unit ball that generalizes the classical Hankel operator. In this paper, we estimate the essential norm of the generalized Hankel operators on the Bergman spaceAp(B)  (p>1)of the unit ball and give an equivalent form of the essential norm.

scholarly journals Commuting Separately Quasihomogeneous Small Hankel Operators on Pluriharmonic Bergman Space

2018 ◽  
Vol 2018 ◽  
pp. 1-7
Author(s):  
Qi Wu ◽  
Chuntao Qin ◽  
Yong Chen ◽  
Yile Zhao
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Hankel Operators ◽  
Quasihomogeneous Symbols

We study (semi)commutativity of small Hankel operators with separately quasihomogeneous symbols on the pluriharmonic Bergman space of the unit ball. Some product problems are also concerned.

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.

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