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Stević, Stevo

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

Appl. Math. Comput. 212, No. 2, 499-504 (2009).
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 \(u\).
Reviewer: Sergey M. Ivashkovich (Villeneuve d’Ascq)

Cited in 39 Documents

MSC:

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

Keywords:

weighted composition operator; Bergman space; weighted-type space; boundedness; compactness
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\textit{S. Stević}, Appl. Math. Comput. 212, No. 2, 499--504 (2009; Zbl 1186.47020)
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