Schatten class of Hankel and Toeplitz operators on the Bergman space of strongly pseudoconvex domains

1995 ◽  
pp. 237-257 ◽  
Author(s):  
Huiping Li ◽  
Daniel H. Luecking
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Pseudoconvex Domains ◽  
Schatten Class ◽  
Strongly Pseudoconvex Domains

scholarly journals Schatten class Toeplitz operators on the parabolic Bergman space II

2012 ◽  
Vol 35 (1) ◽  
pp. 52-77 ◽  
Author(s):  
Masaharu Nishio ◽  
Noriaki Suzuki ◽  
Masahiro Yamada
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Schatten Class

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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