Pointwise Convergence of the Fractional Schrödinger Equation in R2

Chu Hee Cho; Hyerim Ko

doi:10.11650/tjm/210904

Pointwise Convergence of the Fractional Schrödinger Equation in R²

Chu Hee Cho^*
, Hyerim Ko

^*Corresponding author for this work

Department of Mathematics

Seoul National University

Research output: Contribution to journal › Journal article › peer-review

8 Scopus citations

Abstract

We investigate the pointwise convergence of the solution to the fractional Schrödinger equation in R². By establishing H^s(R²) − L³(R²) 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.

Original language	English
Pages (from-to)	177-200
Number of pages	24
Journal	Taiwanese Journal of Mathematics
Volume	26
Issue number	1
DOIs	https://doi.org/10.11650/tjm/210904
State	Published - 2022.02

Keywords

fractional Schrödinger equation
pointwise convergence

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10.11650/tjm/210904

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title = "Pointwise Convergence of the Fractional Schr{\"o}dinger Equation in R2",

abstract = "We investigate the pointwise convergence of the solution to the fractional Schr{\"o}dinger equation in R2. By establishing Hs(R2) − L3(R2) 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.",

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year = "2022",

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language = "English",

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pages = "177--200",

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T1 - Pointwise Convergence of the Fractional Schrödinger Equation in R2

AU - Cho, Chu Hee

AU - Ko, Hyerim

PY - 2022/2

Y1 - 2022/2

N2 - We investigate the pointwise convergence of the solution to the fractional Schrödinger equation in R2. By establishing Hs(R2) − L3(R2) 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.

AB - We investigate the pointwise convergence of the solution to the fractional Schrödinger equation in R2. By establishing Hs(R2) − L3(R2) 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.

KW - fractional Schrödinger equation

KW - pointwise convergence

UR - https://www.scopus.com/pages/publications/85127482386

U2 - 10.11650/tjm/210904

DO - 10.11650/tjm/210904

M3 - Journal article

AN - SCOPUS:85127482386

SN - 1027-5487

VL - 26

SP - 177

EP - 200

JO - Taiwanese Journal of Mathematics

JF - Taiwanese Journal of Mathematics

IS - 1

ER -

Pointwise Convergence of the Fractional Schrödinger Equation in R²

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Keywords

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