Compactification and decompactification by weights on Bergman spaces

2021/07/07 by Lefèvre, Pascal, Li, Daniel, Queffélec, Hervé +1
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2107.03208

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.

Related

• Weighted composition operators on weighted Bergman spaces of bounded symmetric domains
• Boundedness and compactness of Bergman projection commutators in two-weight setting
• Composition operators on the Bergman spaces of a minimal bounded homogeneous domain
• The weighted composition operators on the large weighted Bergman spaces
• Generalized weighted composition operators on Bergman spaces induced by doubling weights