Operator norms and essential norms of weighted composition operators between Banach spaces of analytic functions
Operator norms and essential norms of weighted composition operators between Banach spaces of analytic functions
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DOI：
10.1016/j.jmaa.2015.08.073
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发表时间：
2016-02
影响因子：
1.3
通讯作者：
Flavia Colonna;Maria Tjani
中科院分区：
文献类型：
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作者：
Flavia Colonna;Maria Tjani
在本文中，我们将开单位盘上的一大类解析函数的Banach空间中的有界紧致加权复合算子刻画成加权Banach空间，准确地确定了算子范数，并得到了其本质范数的估计。当这些算子将Hardy空间、加权Bergman空间、Bloch空间和小Bloch空间映射到Banach空间H μ∞（其中权μ是连续函数）时，我们得到了本质范数的精确公式。在这种一般情况下，我们还研究了当目标空间是α- bloch空间时，对于任意α>和更一般地，任意bloch型空间的算子。作为特殊情况，我们导出了作用于Hardy空间和加权Bergman空间的算子的范数和本质范数逼近。直接推论是对某些积分算子的结果。
In this work, we characterize the bounded and compact weighted composition operators from a large class of Banach space of analytic functions on the open unit disk into weighted Banach spaces, determine the operator norm exactly and obtain estimates on the essential norm. We obtain an exact formula of the essential norm when such operators map the Hardy spaces, the weighted Bergman spaces, the Bloch space and the little Bloch space into the Banach space H μ∞(where the weight μ is a continuous function). In this general setting we also study such operators when the target space is an α-Bloch space for any α> 0 and more generally, any Bloch-type space. As special cases, we derive norm and essential norm approximations for the operators acting on the Hardy spaces and the weighted Bergman spaces. Immediate corollaries are results on certain integral operators.