Uniform convergence of the one-dimensional cubic Schrödinger equation

In this article, we investigate the uniform convergence problem of the one-dimensional cubic Schrödinger equation. By using the Kato smoothing estimate, the maximal function estimate and the dyadic mixed Lebesgue spaces, we establish the uniform convergence of the one-dimensional cubic Schrödinger equation in Hs(R)(s>16) which is an alternative proof of Theorem 1.1 (n=1,p=3) of Compaan et al. [Pointwise convergence of the Schrödinger flow. Int Math Res Not. 2021;1:596–647].