Toeplitz Operators on the Harmonic Bergman Space with Pseudodifferential Defining Symbols

2015 ◽  
pp. 591-603
Author(s):  
Maribel Loaiza ◽  
Nikolai Vasilevski
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Harmonic Bergman Space

scholarly journals Positive Toeplitz Operators of Schatten–Herz Type

2007 ◽  
Vol 185 ◽  
pp. 31-62 ◽  
Author(s):  
Boorim Choe ◽  
Hyungwoon Koo ◽  
Kyunguk Na
Keyword(s):  
Recent Work ◽  
Bergman Space ◽  
Toeplitz Operators ◽  
Harmonic Bergman Space ◽  
Berezin Transforms ◽  
Averaging Functions ◽  
Positive Toeplitz Operators

AbstractMotivated by a recent work of Loaiza et al. for the holomorphic case on the disk, we introduce and study the notion of Schatten-Herz type Toeplitz operators acting on the harmonic Bergman space of the ball. We obtain characterizations of positive Toeplitz operators of Schatten-Herz type in terms of averaging functions and Berezin transforms of symbol functions. Our characterization in terms of Berezin transforms settles a question posed by Loaiza et al.

scholarly journals Commuting Toeplitz operators on the harmonic Bergman space.

1999 ◽  
Vol 46 (1) ◽  
pp. 163-174 ◽  
Author(s):  
Boo Rim Choe ◽  
Young Joo Lee
Keyword(s):  
Bergman Space ◽  
Toeplitz Operators ◽  
Harmonic Bergman Space
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