The Wk,p-continuity of wave operators for Schrödinger operators

Introduction, Theorems. For the pair of Schr\"odinger operators H₀=D₁²+⋯+Dₘ² and H=H₀+V , where Dⱼ=-i∂/∂ xⱼ, $j=1,$ ⋯ , m , and V is the multiplication operator with the real valued function $V(x)$ , the wave operators W±=W±(H, H₀) are defined by