  We generalize the Abstract Interpolation Lemma proved by the authors in [2].
Using this extension, we show in a more general context, the persistence
property for the generalized Korteweg-de Vries equation, see (1.2), in the
weighted Sobolev space with low regularity in the weight. The method used can
be applied for other nonlinear dispersive models, for instance the
multidimensional nonlinear Schrodinger equation.
