A remark on admissible triples for the generalized KdV equation

In this paper we give a condition of type L x p L T q , under which the solution u ( t ) of the generalized KdV equation satisfies for any θ ∈ ( − 1 , 1 ) , for any admissible triples ( p 1 , q 1 , α 1 ) the following inequality | D x α 1 + θ u ( t ) | L x p 1 L T q 1 ≤ c | D x θ u ( 0 ) | L 2 . We also present a global well-posedness result in some spaces of admissible triples.