A Note on Non-tangential Convergence for Schr\'{o}dinger Operators

Autor:	Li, Wenjuan, Wang, Huiju, Yan, Dunyan
Rok vydání:	2020
Předmět:	Mathematics - Classical Analysis and ODEs 42B20 42B25 35S10
Druh dokumentu:	Working Paper
Popis:	The goal of this note is to establish non-tangential convergence results for Schr\"{o}dinger operators along restricted curves. We consider the relationship between the dimension of this kind of approach region and the regularity for the initial data which implies convergence. As a consequence, we obtain a upper bound for $p$ such that the Schr\"{o}dinger maximal function is bounded from $H^{s}(\mathbb{R}^{n})$ to $L^{p}(\mathbb{R}^{n})$ for any $s > \frac{n}{2(n+1)}$.
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2008.03093 Zobrazit plný text záznamu View this record from Arxiv