Weighted Composition Operators on Bergman and Dirichlet Spaces |
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Authors: | Mirzakarimi G Seddighi K |
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Institution: | (1) Department of Mathematics, Shiraz University, Shiraz, Iran |
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Abstract: | Let H() denote a functional Hilbert space of analytic functions on a domain . Let w : C and : be such that w f is in H() for every f in H(). The operator wC
given by f w f is called a weighted composition operator on H(). In this paper we characterize such operators and those for which (wC
)* is a composition operator. Compact weighted composition operators on some functional Hilbert spaces are also characterized. We give sufficient conditions for the compactness of such operators on weighted Dirichlet spaces. |
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Keywords: | Weighted composition operator compact functional Hilbert space Carleson measure angular derivative Dirichlet space |
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