Toeplitz operators on Bergman spaces with exponential weights

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