Compact Composition Operators on BMOA
Compact Composition Operators on BMOA
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DOI：
10.1090/s0002-9947-99-02387-9
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发表时间：
1999-02
影响因子：
1.3
通讯作者：
P. Bourdon;J. Cima;A. Matheson
中科院分区：
文献类型：
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作者：
P. Bourdon;J. Cima;A. Matheson
.我们刻画了BMOA上的紧致复合算子，BMOA是由开单位圆盘U上的全纯函数组成的空间，这些全纯函数是BMOA U上函数的Poisson积分，具有有界平均振荡。然后，我们使用我们的特征表明，紧性的BMOA上的复合算子意味着它的紧性的哈代空间（一个简单的例子表明，匡威不成立）。我们还探讨了复合算子C φ：BMOA → BMOA的紧性如何与φ（U）在φ U附近的形状相关，引入了平均接触阶的概念。最后讨论了BMOA、VMOA及大小Bloch空间上复合算子紧性条件之间的关系。
. We characterize the compact composition operators on BMOA, the space consisting of those holomorphic functions on the open unit disk U that are Poisson integrals of functions on ∂U , that have bounded mean oscillation. We then use our characterization to show that compactness of a composition operator on BMOA implies its compactness on the Hardy spaces (a simple example shows the converse does not hold). We also explore how compactness of the composition operator C φ : BMOA → BMOA relates to the shape of φ ( U ) near ∂U , introducing the notion of mean order of contact . Finally, we discuss the relationships among compactness conditions for composition operators on BMOA, VMOA, and the big and little Bloch spaces.