A note on some variations of the maximal inequality for the fractional Schrödinger equation

The purpose of this note is to provide a summary of the recent work of the authors on two variations of the pointwise convergence problem for the solutions to the fractional Schr\"odinger equations; convergence along a tangential line and along a set of lines, as exhibiting some new results in...

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Bibliographic Details
Published inarXiv.org
Main Authors Chu-hee, Cho, Shiraki, Shobu
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 23.12.2022
Subjects
Convergence
Schrodinger equation
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Summary:The purpose of this note is to provide a summary of the recent work of the authors on two variations of the pointwise convergence problem for the solutions to the fractional Schr\"odinger equations; convergence along a tangential line and along a set of lines, as exhibiting some new results in each setting. For the former case, we make a simple observation on a path along a tangential curve of exponential order. We discuss counterexamples for the latter case that show some of the known smooth regularities are essentially optimal.
ISSN:2331-8422