Large data mass-subcritical NLS: critical weighted bounds imply scattering

Abstract: We consider the mass-subcritical nonlinear Schr\"odinger equation in all space dimensions with focusing or defocusing nonlinearity. For such equations with critical regularity $s_c\in(\max{-1,-\frac{d}{2}},0)$, we prove that any solution satisfying $|\, |x|^{|s_c|}e^{-it\Delta} u|_{L_t^\infty L_x^2} <\infty$ on its maximal interval of existence must be global and scatter.