Pointwise Convergence for sequences of Schr\'{o}dinger means in $\mathbb{R}^{2}$

Autor:	Li, Wenjuan, Wang, Huiju, Yan, Dunyan
Rok vydání:	2020
Předmět:	Mathematics - Classical Analysis and ODEs 42B20 42B25 35S10
Druh dokumentu:	Working Paper
Popis:	We consider pointwise convergence of Schr\"{o}dinger means $e^{it_{n}\Delta}f(x)$ for $f \in H^{s}(\mathbb{R}^{2})$ and decreasing sequences $\{t_{n}\}_{n=1}^{\infty}$ converging to zero. The main theorem improves the previous results of [Sj\"{o}lin, JFAA, 2018] and [Sj\"{o}lin-Str\"{o}mberg, JMAA, 2020] in $\mathbb{R}^{2}$. This study is based on investigating properties of Schr\"{o}dinger type maximal functions related to hypersurfaces with vanishing Gaussian curvature.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2010.08701 Zobrazit plný text záznamu View this record from Arxiv