Weighted composition operators between Dirichlet spaces |
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Authors: | Wang Maofa |
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Affiliation: | School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China |
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Abstract: | In this article, we study the boundedness of weighted composition operators between different vector-valued Dirichlet spaces. Some sufficient and necessary conditions for such operators to be bounded are obtained exactly, which are different completely from the scalar-valued case. As applications, we show that these vector-valued Dirichlet spaces are different counterparts of the classical scalar-valued Dirichlet space and characterize the boundedness of multiplication operators between these different spaces. |
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Keywords: | Vector-valued analytic function Dirichlet space weighted composition operator boundedness |
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