Global theory for NLS in the weighted spaces II: final data problem

In this paper, we study the final data problem for the defocusing nonlinear Schrödinger equation (NLS) $$ i\partial_t u + \frac12Δu = |u|^p u $$ in weighted spaces $\dotΣ^s(\mathbb R^d):=L_x^2(\mathbb R^d;|x|^{2s}\mathrm{d} x)$. Let $s_c=\frac d2-\frac2p$. Under the scaling of the NLS, $\dotΣ^{-s_c}