Compactification and decompactification by weights on Bergman spaces

Pascal Lefèvre (1) , Daniel Li (2) , Hervé Queffélec (3) , Luis Rodriguez-Piazza (4)

1 LML - Laboratoire de Mathématiques de Lens
2 UA - Université d'Artois
3 Université de Lille
4 Universidad de Sevilla / University of Sevilla

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.

Domains: Functional Analysis [math.FA]

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