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arXiv · 2207.09219

Pointwise convergence of sequential Schr\"odinger means

Chu-Hee Cho·Hyerim Ko·Youngwoo Koh·Sanghyuk Lee
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Abstract

We study pointwise convergence of the fractional Schr\"odinger means along sequences $t_n$ which converge to zero. Our main result is that bounds on the maximal function $\sup_{n} |e^{it_n(-\Delta)^{\alpha/2}} f| $ can be deduced from those on $\sup_{0<t\le 1} |e^{it(-\Delta)^{\alpha/2}} f|$ when $\{t_n\}$ is contained in the Lorentz space $\ell^{r,\infty}$. Consequently, our results provide seemingly optimal results in higher dimensions, which extend the recent work of Dimou-Seeger, and Li-Wang-Yan to higher dimensions. Our approach based on a localization argument also works for other dispersive equations and provides alternative proofs of previous results on sequential convergence.

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Chu-Hee Cho, Hyerim Ko, Youngwoo Koh, Sanghyuk Lee. 2022-07-19. Pointwise convergence of sequential Schr\"odinger means. https://arxiv.org/abs/2207.09219

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