Compactification and decompactification by weights on Bergman spaces

Abstract

We characterize the symbols $\hat{I}¦$ for which there exists a weight w such that the weighted composition operator M w C $\hat{I}¦$ is compact on the weighted Bergman space B 2 $\hat{I}\pm$. We also characterize the symbols for which there exists a weight w such that M w C $\hat{I}¦$ is bounded but not compact. We also investigate when there exists w such that M w C $\hat{I}¦$ is Hilbert-Schmidt on B 2 $\hat{I}\pm$.