In this article, we consider the kinetic derivative nonlinear Schrödinger equation (KDNLS), which is a one-dimensional nonlinear Schrödinger equation with a cubic derivative nonlinear term containing the Hilbert transformation. For the Cauchy problem, both on the real line and on the circle, we apply the short-time Fourier restriction method to establish a priori estimate for small and smooth solutions in Sobolev spaces \(H^{s}\) with \(s>1/4\).

中文翻译：

---

通过短时傅立叶限制方法对 KDNLS 进行低规律性先验估计

在本文中，我们考虑动力学导数非线性薛定谔方程 (KDNLS)，它是一个一维非线性薛定谔方程，具有包含希尔伯特变换的三次导数非线性项。对于柯西问题，无论是在实线上还是在圆上，我们都应用短时傅立叶限制方法来建立索伯列夫空间\(H^{s}\)中小而光滑解的先验估计，其中\(s >1/4\)。