Toeplitz Operators with BMO Symbols on the Weighted Bergman Space of the Unit Ball

In this paper we prove that the boundedness and compactness of Toeplitz operator with a BMOα1 symbol on the weighted Bergman space Aα2（Bn） of the unit ball is completely determined by the behavior of its Berezin transform, where ≥ -1 and n 〉 1.

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 27; no. 11; pp. 2129 - 2142
Main Authors Zhang, Kan, Liu, Chao Mei, Lu, Yu Feng
Format Journal Article
LanguageEnglish
Published Heidelberg Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 01.11.2011
Springer Nature B.V
Subjects
Berezin变换
BMO
Mathematical analysis
Mathematics
Mathematics and Statistics
Operators
Studies
Symbols
Toeplitz算子
Transforms
加权Bergman空间
单位球
建筑物
有界性
管理条例
32A37
Berezin transform
Toeplitz operator
BMO
47B35
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Summary:In this paper we prove that the boundedness and compactness of Toeplitz operator with a BMOα1 symbol on the weighted Bergman space Aα2（Bn） of the unit ball is completely determined by the behavior of its Berezin transform, where ≥ -1 and n 〉 1.
Bibliography:In this paper we prove that the boundedness and compactness of Toeplitz operator with a BMOα1 symbol on the weighted Bergman space Aα2（Bn） of the unit ball is completely determined by the behavior of its Berezin transform, where ≥ -1 and n 〉 1.
11-2039/O1
Toeplitz operator, BMO, Berezin transform
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ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-011-0038-3