On small data scattering of Hartree equations with short-range interaction

Abstract

In this note we study Hartree type equations with $|\nabla|^\alpha (1 \frac{2-\alpha}2$ when $2 < \gamma_1 \le d$ and $0 < \gamma_2 \le 2$. For this we use $U^p-V^p$ space argument and Strichartz estimates.