Toeplitz Operators on the Unit Ball with Locally Integrable Symbols
Toeplitz Operators on the Unit Ball with Locally Integrable Symbols
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DOI：
10.1007/s00020-022-02695-3
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发表时间：
2020-11
影响因子：
0.8
通讯作者：
Raffael Hagger;Cong Liu;J. Taskinen;J. Virtanen
中科院分区：
文献类型：
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作者：
Raffael Hagger;Cong Liu;J. Taskinen;J. Virtanen
我们研究了单位球上的加权调和伯格曼空间上具有局部可积符号的托普利茨算子的有界性。概括解析函数空间的早期结果，我们根据其符号的适当平均值导出了有界性的一般充分条件。我们还获得了类似的紧致性“消失”条件。最后，我们展示了如何将这些结果转移到解析函数的标准加权伯格曼空间的设置中。
We study the boundedness of Toeplitz operatorswith locally integrable symbols on weighted harmonic Bergman spaces over the unit ball of. Generalizing earlier results for analytic function spaces, we derive a general sufficient condition for the boundedness ofin terms of suitable averages of its symbol. We also obtain a similar “vanishing” condition for compactness. Finally, we show how these results can be transferred to the setting of the standard weighted Bergman spaces of analytic functions.