A decay property of solutions to the k-generalized KdV equation

We use a Leibnitz rule type inequality for fractional derivatives to prove conditions under which a solution $u(x,t)$ of the k-generalized KdV equation is in the space $L^2(\mathrm{\mid }x{\mathrm{\mid }}^{2s}dx)$ for $s\in {\mathbb{R}}_{+}$.