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arXiv · 2212.12373

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

Chu-hee Cho·Shobu Shiraki
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Abstract

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 Schrödinger 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.

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Chu-hee Cho, Shobu Shiraki. 2022-12-23. A note on some variations of the maximal inequality for the fractional Schrödinger equation. https://arxiv.org/abs/2212.12373

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