## Weighted composition operators from weighted Bergman spaces to weighted-type spaces on the unit ball.(English)Zbl 1186.47020

If $$H(\Delta)$$ denote the space of holomorphic functions in the unit disc $$\Delta\subset\mathbb{C}^n$$. For a holomorphic self-map $$\varphi= \Delta\to\Delta$$ and $$u\in H(\Delta)$$, the author considers the composition operator $C_{\varphi,u}: f\mapsto uf(\varphi).$ The main goal of the paper is to compute the norm of $$C_{\varphi,u}$$ in different weighted spaces of holomorphic functions in terms of function theoretic properties of $$\varphi$$ and $$u$$.

### MSC:

 47B33 Linear composition operators 46E15 Banach spaces of continuous, differentiable or analytic functions 32A36 Bergman spaces of functions in several complex variables
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### References:

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