In this Note, we consider problems of endpoint Strichartz estimates for the kinetic equation in one dimension. The fundamental result obtained in Theorem 1 is proved using two different methods: in the first we construct an explicit counterexample; in the second uses a duality argument. To cite this article: Z. Guo, L. Peng, C. R. Acad. Sci. Paris, Ser. I 345 (2007).