A note on the Schrodinger maximal function

It is shown that control of the Schrodinger maximal functions ${\sup }_{0<t<1}\mathrm{\mid }{e}^{it\mathrm{\Delta }}f\mathrm{\mid }$ for $f\in H^s({\mathbb{R}}^n)$ requires $s\geq \frac n{2(n+1)}$