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Compactification and decompactification by weights on Bergman spaces

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Pascal Lefèvre
Daniel Li
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Hervé Queffélec
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Abstract

We characterize the symbols ϕ for which there exists a weight w such that the weighted composition operator M w C ϕ is compact on the weighted Bergman space B 2 α. We also characterize the symbols for which there exists a weight w such that M w C ϕ is bounded but not compact. We also investigate when there exists w such that M w C ϕ is Hilbert-Schmidt on B 2 α.
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Dates and versions

hal-03277079 , version 1 (07-07-2021)

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Pascal Lefèvre, Daniel Li, Hervé Queffélec, Luis Rodriguez-Piazza. Compactification and decompactification by weights on Bergman spaces. 2021. ⟨hal-03277079⟩
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