Distance of a Bloch Function to the Little Bloch Space
Distance of a Bloch Function to the Little Bloch Space
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DOI：
10.1017/s0004972700047493
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发表时间：
2006-01
影响因子：
0.7
通讯作者：
Maria Tjani
中科院分区：
文献类型：
--
作者：
Maria Tjani
受P.Jones给出的布洛赫函数到有界平均振荡空间BMOA的距离公式的启发，我们得到了布洛赫函数到小布洛赫空间β0的距离的几个公式。立即结果是β0中函数的等价表达式。我们还给出了几个具体函数到β0的距离的例子。我们讨论了到β0的距离与Bloch空间上某些复合算子的本质范数β之间的关系。最后，我们证明了β中的距离公式具有Bloch型空间的相似性。
Motivated by a formula of P. Jones that gives the distance of a Bloch function to BMOA, the space of bounded mean oscillations, we obtain several formulas for the distance of a Bloch function to the little Bloch space, β0. Immediate consequences are equivalent expressions for functions in β0. We also give several examples of distances of specific functions to β0. We comment on connections between distance to β0 and the essential norm of some composition operators on the Bloch space, β. Finally we show that the distance formulas in β have Bloch type spaces analogues.