Embedding and compact embedding of weighted Bergman spaces

Abstract

We use embeddings of Bergman spaces and fractional radial differential operators to study the $L_{\mathit{\alpha }}^p$–$L_{\mathit{\beta }}^q$ mapping properties of Bergman-type projections on the open unit ball of ${\mathbb{C}}^n$. We recover and extend several existing results in this direction. In particular, this approach allows us to treat the cases when $0<q<1$ and $\mathit{\alpha }\le -1$. We also characterize when the embedding of one weighted Bergman space into another is compact.