Compactification and decompactification by weights on Bergman spaces - Lefèvre, Pascal; Li, Daniel; Queffélec, Hervé; Rodríguez-Piazza, Luis (Journal of mathematical analysis and applications, 2022)
We characterize the symbols φ for which there exists a weight w such that the weighted composition operator MwCφ is compact on the weighted Bergman space Bα2. We also characterize the symbols for which there exists a weight w such that MwCφ is bounded but not compact. We also investigate when there exists w such that MwCφ is Hilbert-Schmidt on Bα2.