$L^p$-estimates of maximal function related to Schr{o}dinger Equation in $mathbb{R}^2$

Using Guths polynomial partitioning method, we obtain $L^p$ estimates for the maximal function associated to the solution of Schrodinger equation in $mathbb R^2$. The $L^p$ estimates can be used to recover the previous best known result that $lim_{t to 0} e^{itDelta}f(x)=f(x)$ almost everywhere for all $f in H^s (mathbb{R}^2)$ provided that $s>3/8$.