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

@article{Killip2016LargeDM,
  title={Large data mass-subcritical NLS: critical weighted bounds imply scattering},
  author={Rowan Killip and Satoshi Masaki and Jason Murphy and Monica Visan},
  journal={Nonlinear Differential Equations and Applications NoDEA},
  year={2016},
  volume={24},
  pages={1-33}
}
We consider the mass-subcritical nonlinear Schrödinger equation in all space dimensions with focusing or defocusing nonlinearity. For such equations with critical regularity $$s_c\in (\max \{-1,-\frac{d}{2}\},0)$$sc∈(max{-1,-d2},0), we prove that any solution satisfying $$\begin{aligned} \left\| \, |x|^{|s_c|}e^{-it\Delta } u\right\| _{L_t^\infty L_x^2} <\infty \end{aligned}$$|x||sc|e-itΔuLt∞Lx2<∞on its maximal interval of existence must be global and scatter. 
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