Open Access
February, 2022 Pointwise Convergence of the Fractional Schrödinger Equation in $\mathbb{R}^2$
Chu-Hee Cho, Hyerim Ko
Author Affiliations +
Taiwanese J. Math. 26(1): 177-200 (February, 2022). DOI: 10.11650/tjm/210904


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 [19]. Our estimates extend the refined Strichartz estimates obtained by Du, Guth, and Li [10] to a general class of elliptic functions.

Funding Statement

This work was supported by NRF grant no. 2021R1A2B5B02001786, 2020R1I1A1A01072942 (C. Cho) 2017R1D1A1A02019547, and 2019R1A6A3A01092525 (H. Ko), South Korea.


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Chu-Hee Cho. Hyerim Ko. "Pointwise Convergence of the Fractional Schrödinger Equation in $\mathbb{R}^2$." Taiwanese J. Math. 26 (1) 177 - 200, February, 2022.


Received: 18 June 2021; Revised: 22 August 2021; Accepted: 14 September 2021; Published: February, 2022
First available in Project Euclid: 19 October 2021

MathSciNet: MR4367790
Digital Object Identifier: 10.11650/tjm/210904

Primary: 35Q41

Keywords: fractional Schrödinger equation , pointwise convergence

Rights: Copyright © 2022 The Mathematical Society of the Republic of China

Vol.26 • No. 1 • February, 2022
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