Embedding theorems and integration operators on Bergman spaces with rapidly decreasing weights

We completely describe those positive Borel measures μ   in the unit disc DD such that the Bergman space Ap(w)⊂Lq(μ)Ap(w)⊂Lq(μ), 00α>0, and some double exponential type weights.As an application of that result, we characterize the boundedness and the compactness of Tg:Ap(w)→Aq(w)Tg:Ap(w)→Aq(w), 0