Improved local smoothing estimate for the fractional Schrödinger operator

Abstract

In this paper, we consider the local smoothing estimate of fractional Schrödinger operator $e^{it(-\Delta {)}^{\alpha /2}}$ with $\alpha >1$. Using the $k$-broad "norm" estimate developed by Guth, we improve the previous best results of local smoothing estimate for the fractional Schrödinger operator .

To appear in Bulletin of the London Mathematical Society