Toeplitz operators on Bergman spaces with exponential weights

Abstract

In this paper, we focus on the weighted Bergman spaces A p ϕ in D with ϕ ∈ W 0 . We first give characterizations of those finite positive Borel measures µ in D such that the embedding A p ϕ ⊂ L q µ is bounded or compact for 0 < p, q < ∞. Then we describe bounded or compact Toeplitz operators T µ from one Bergman space A p ϕ to another A q ϕ for all possible 0 < p, q < ∞. Finally, we characterize Schatten class Toeplitz operators on A 2 ϕ .