Improved local smoothing estimate for the fractional Schr\"odinger operator

In this paper, we consider the local smoothing estimate of fractional Schr"{o}dinger operator $e^{it(-\mathrm{\Delta }{)}^{\alpha \mathrm{/}2}}$ 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 Schr"{o}dinger operator .