Toeplitz Operators on Generalized Bergman Spaces
Toeplitz Operators on Generalized Bergman Spaces
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DOI：
10.1007/s00020-009-1734-6
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发表时间：
2009-03
影响因子：
0.8
通讯作者：
Kamthorn Chailuek;B. Hall
中科院分区：
文献类型：
--
作者：
Kamthorn Chailuek;B. Hall
我们考虑加权Bergman空间，其中τ是双曲体积测度。这些空间是非零的，当且仅当λ >d。对于0 < λ ≤d，具有相同再生核公式的空间可以使用Sobolev型范数定义。我们在这些广义Bergman空间上定义了Toeplitz算子并研究了它们的性质。具体来说，我们描述了相应的Toeplitz算子可以定义为有界算子或广义Bergman空间上的希尔伯特-施密特算子的符号类。
We consider the weighted Bergman spaces, where we set, withτbeing the hyperbolic volume measure. These spaces are nonzero if and only if λ >d. For 0 < λ ≤d, spaces with the same formula for the reproducing kernel can be defined using a Sobolev-type norm. We define Toeplitz operators on these generalized Bergman spaces and investigate their properties. Specifically, we describe classes of symbols for which the corresponding Toeplitz operators can be defined as bounded operators or as a Hilbert–Schmidt operators on the generalized Bergman spaces.