Weighted composition operators on weighted Bergman spaces of the unit ball

Suppose Φ is an analytic self map of B _n and φ is analytic on B _n. Then a weighted composition operator induced by Φ with weight φ is given by (W _φ,ρf) (z) = φ(z)f(Φ(z)) for z in B _n and f analytic on B _n. Given W _φ,Φ: A ^p _α(B _n) → A ^q _βj(B _n) we characterize boundedness and compactness of W _φ,ρ, where 0 p,q < ∞ and -1 < α, β < ∞. We also characterize the Schatten p-class weighted composition operators S _p (A ² _α(B _n)) for 0 < p < ∞ and -1< α < ∞.