Composition operators with maximal norm on weighted bergman spaces
Composition operators with maximal norm on weighted bergman spaces
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DOI：
10.1090/s0002-9939-06-08271-2
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发表时间：
2006-02
期刊：
影响因子：
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通讯作者：
Brent J. Carswell;Christopher N. B. Hammond
中科院分区：
文献类型：
--
作者：
Brent J. Carswell;Christopher N. B. Hammond
证明了加权Bergman空间A2α(特别是A2=A2 0)上的任何具有极大范数的复合算子都是由圆盘自同构或固定原点的映射诱导的.这一结果证明了加权Bergman空间和Hardy空间H2之间的一个重要区别，即每个内函数都诱导出一个范数最大的复合算子。
We prove that any composition operator with maximal norm on one of the weighted Bergman spaces A 2 α (in particular, on the space A 2 = A 2 0 ) is induced by a disk automorphism or a map that fixes the origin. This result demonstrates a major difference between the weighted Bergman spaces and the Hardy space H 2 , where every inner function induces a composition operator with maximal norm.