A note on the quartic generalized Korteweg-de Vries equation in weighted Sobolev spaces

In this paper we establish the persistence property for solutions of the quartic generalized Korteweg-de Vries equation with initial data in weighted Sobolev spaces $H^s(\mathbb{R})\cap L^2(\mathrm{\mid }x{\mathrm{\mid }}^{2r}dx)$ for $s=1\mathrm{/}12+\epsilon$ and any $r\in (0,R)$, for some $0<\epsilon <1\mathrm{/}4$ and $0<R<s\mathrm{/}2$.