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The Cauchy problem for the derivative nonlinear Schrödinger equation with periodic boundary condition is considered. Local well-posedness for data u 0 in the space b H s r (T), defined by the norms u 0 b H s r (T) = ξ s b u 0 ℓ r ′ ξ , is shown in the parameter range s ≥ 1 2 , 2 > r > 4 3. The proof is based on an adaptation of the gauge transform to the… (More)

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