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In this paper we show the persistence property for solutions of thederivative nonlinear Schr\"odinger equation with initial data in weightedSobolev spaces $H^{2}(\mathbb{R})\cap L^2(|x|^{2r}dx)$, $r\in (0,1]$.

Persistence of solutions to the Derivative Nonlinear Schr\"odinger equation in weighted Sobolev spaces