## 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 $$B_\alpha$$.
Reviewer: Kehe Zhu (Albany)

### MSC:

 30D45 Normal functions of one complex variable, normal families 47B33 Linear composition operators

### Keywords:

Lipschitz space; Bloch space
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