Schatten Class Hankel Operators on the Bergman Space of the Unit Ball

1991 ◽  
Vol 113 (1) ◽  
pp. 147 ◽  
Author(s):  
Kehe Zhu
Keyword(s):  
Unit Ball ◽  
Bergman Space ◽  
Hankel Operators ◽  
Schatten Class

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.

scholarly journals Schatten Class Operators in ℒ(La2(ℂ+)) \msbm=MTMIB${\cal L}\left( {L_a^2 \left( {{\msbm C}_+ } \right)} \right)$

2017 ◽  
Vol 55 (2) ◽  
pp. 91-117
Author(s):  
Namita Das ◽  
Jitendra Kumar Behera
Keyword(s):  
Bergman Space ◽  
Half Plane ◽  
Toeplitz Operators ◽  
Hankel Operators ◽  
Bounded Operators ◽  
Area Measure ◽  
Schatten Class ◽  
The Right

AbstractIn this paper, we consider Toeplitz operators defined on the Bergman space\msbm=MTMIB$L_a^2 \left( {{\msbm C}_+ } \right)$of the right half plane and obtain Schatten class characterization of these operators. We have shown that if the Toeplitz operators 𝕿φon\msbm=MTMIB$L_a^2 \left( {{\msbm C}_+ } \right)$belongs to the Schatten classSp, 1 ≤p < ∞,then\msbm=MTMIB$\tilde \phi \in L^p \left( {{\msbm C}_+ ,d\nu } \right)$, where$\tilde \phi \left( w \right) = \left\langle {\phi b_{\bar w} ,b_{\bar w} } \right\rangle $w ∈ℂ+and$b_{\bar w} (s) = {1 \over {\sqrt \pi }}{{1 + w} \over {1 + \bar w}}{{2 Rew} \over {\left( {s + w} \right)^2 }}$. Here$d\nu (w) = \left| {B(\bar w,w)} \right|d\mu (w)$, wheredμ(w) is the area measure on ℂ+and$B(\bar w,w) = \left( {b_{\bar w} (\bar w)} \right)^2 $: Furthermore, we show that ifφ ∈ Lp(ℂ+,dv),then\msbm=MTMIB$\tilde \phi \in L^p ({\msbm C}_+ ,d\nu )$and 𝕿φ∈Sp. We also use these results to obtain Schatten class characterizations of little Hankel operators and bounded operators defined on the Bergman space\msbm=MTMIB$L_a^2 \left( {{\msbm C}_+ } \right)$

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