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DOI: 10.46698/p4238-0191-2122-t Bounded Composition Operators on Weighted Function Spaces in the Unit Disk
Abstract:
We introduce a general class of weighted spaces \(\mathcal{H}(\beta)\) of holomorphic functions in the unit disk \(\mathbb{D}\), which contains several classical spaces, such as Hardy space, Bergman space, Dirichlet space. We characterize boundedness of composition operators \(C_{\varphi}\) induced by affine and monomial symbols \(\varphi\) on these spaces \(\mathcal{H}(\beta)\). We also establish a sufficient condition under which the operator \(C_{\varphi}\) induced by the symbol \(\varphi\) with relatively compact image \(\varphi(\mathbb{D})\) in \(\mathbb{D}\) is bounded on \(\mathcal{H}(\beta)\). Note that in the setting of \(\mathcal{H}(\beta)\), the characterizations of boundedness of composition operators \(C_{\varphi}\) depend closely not only on functional properties of the symbols \(\varphi\) but also on the behavior of the weight sequence \(\beta\).
Keywords: composition operator, weighted space, weight sequence, holomorphic function, unit disk
Language: English
For citation: Hua, S., Khoi, L. H. and Tien, P. T. Bounded Composition Operators on Weighted Function Spaces in the Unit Disk,
Vladikavkaz Math. J., 2020, vol. 22, no. 3, pp.112-123. DOI 10.46698/p4238-0191-2122-t
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