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Essential norms of weighted composition operators between Bloch-type spaces. (English) Zbl 1061.30023
For $\alpha>0$ let $B_\alpha$ denote the space of analytic functions $f$ in the unit disk $D$ such that $\sup_{x\in D}(1-|z|^2)^\alpha |f'(z)|<\infty$. For an analytic function $u$ in $D$ and an analytic selfmap $\varphi$ of $D$ the paper studies the weighted composition operator $C$ defined on $B_\alpha$ as follows: $Cf=u f(\varphi)$, $f\in B_\alpha$. The main result of the paper is a formula for the essential norm of $C$ on $B_\alpha$.

30D45Bloch functions, normal functions, normal families
47B33Composition operators
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