Pointwise convergence of the fractional Schrödinger equation in ${\mathbb{R}}^2$

Abstract

We investigate the pointwise convergence of the solution to the fractional Schrödinger equation in ${\mathbb{R}}^2$. By establishing $H^s({\mathbb{R}}^2)-L^3({\mathbb{R}}^2)$ estimates for the associated maximal operator provided that $s>1/3$, we improve the previous result obtained by Miao, Yang, and Zheng. Our estimates extend the refined Strichartz estimates obtained by Du, Guth, and Li to a general class of elliptic functions.

arXiv comment20 pages

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