论文标题
顺序schrödinger平均值的侧面收敛
Pointwise convergence of sequential Schrödinger means
论文作者
论文摘要
我们研究了分数schrödinger的指数融合，沿序列$ t_n $融合到零。我们的主要结果是最大函数上的界限$ \ sup_ {n} | e^{it_n（-Δ）^{α/2}} f | $可以从$ \ sup_ {0 <t \ le 1} | e^{it（-Δ）^{α/2}} f | $中的$中推导，当$ \ {t_n \} $中包含在lorentz space $ \ ell^ell^{r，\ f，\ iffty} $中。因此，我们的结果在较高的维度中似乎提供了最佳的结果，这些结果将dimou-seeger的最新工作和li-wang-yan扩展到更高的维度。我们基于本地化参数的方法还适用于其他分散方程，并为顺序收敛提供了先前结果的替代证明。
We study pointwise convergence of the fractional Schrödinger means along sequences $t_n$ which converge to zero. Our main result is that bounds on the maximal function $\sup_{n} |e^{it_n(-Δ)^{α/2}} f| $ can be deduced from those on $\sup_{0<t\le 1} |e^{it(-Δ)^{α/2}} f|$ 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.
