Persistence of solutions to the Derivative Nonlinear Schrödinger equation in weighted Sobolev spaces

In this paper we show the persistence property for solutions of the derivative nonlinear Schrödinger equation with initial data in weighted Sobolev spaces $H^2(\mathbb{R})\cap L^2(\mathrm{\mid }x{\mathrm{\mid }}^{2r}dx)$, $r\in (0,1]$.