Bergman空间上复合算子的范数与本性范数
Norm and Essential Norm of Composition Operator on Bergman Space
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摘要: 用D表示单位圆盘, A^p(D)表示D上的Bergman空间. 设\varphi是D上的解析自映射. 定义复合算子C_\varphi: (C_\varphi f)(z)=f(\varphi(z)). 研究了A^p(D)上复合算子的 KSP 性质. 同时,计算了D上Bergman空间上一些复合算子的范数与本性范数. (C_\varphi f)(z)=f(\varphi(z)) . 作者研究了A^p(D)上复合算子的 KSP 性质. 同时, 作者还计算了D上Bergman空间上一些复合算子的范数与本性范数.Abstract: Let D be the unit disk, A^p(D) be the Bergman space in D and \varphi be an analytic self-map of D. The composition operator C_\varphi is defined as (C_\varphi f)(z)=f(\varphi(z)) . Then the property of KSP of the composition operator on A^p(D) is investigated, and the norm and the essential norm of some composition operators on Bergman spaces on D are calculated.
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