Toeplitz operators on weighted Bergman spaces on finitely connected domains

We study the weighted Bergman spaces on finitely connected planar domains. They are isomorphic to the product of weighted Bergman spaces on the unit disk. Using this, we characterize the Carleson embeddings and prove kernel estimates. We characterize bounded, compact and Schatten class composition and Toeplitz operators on these spaces. Our results generalize several recent ones in the unit disk or simply connected case