A remark on admissible triples for the generalized KdV equation

In this paper we give a condition of type LxpLTq, under which the solution u(t)u(t) of the generalized KdV equation satisfies for any θ∈(−1,1)θ∈(−1,1), for any admissible triples (p1,q1,α1)(p1,q1,α1) the following inequality |Dxα1+θu(t)|Lxp1LTq1≤c|Dxθu(0)|L2. We also present a global well-posedness result in some spaces of admissible triples.