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arXiv · 1809.03246

Pointwise convergence of the fractional Schr\"odinger equation in $\mathbb R^2$

Chu-hee Cho·Hyerim Ko
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Abstract

We investigate the pointwise convergence of the solution to the fractional Schr\"odinger 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.

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Chu-hee Cho, Hyerim Ko. 2018-09-10. Pointwise convergence of the fractional Schr\"odinger equation in $\mathbb R^2$. https://arxiv.org/abs/1809.03246

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