A note on endpoint $L^p$-continuity of wave operators for classical and higher order Schr\'odinger operators
| Autor: | Erdogan, M. Burak, Green, William R. |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1016/j.jde.2023.01.028 |
| Popis: | We consider the higher order Schr\"odinger operator $H=(-\Delta)^m+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2m$, $m\in \mathbb N$. We adapt our recent results for $m>1$ to show that the wave operators are bounded on $L^p(\mathbb R^n)$ for the full the range $1\leq p\leq \infty$ in both even and odd dimensions without assuming the potential is small. The approach used works without distinguishing even and odd cases, captures the endpoints $p=1,\infty$, and somehow simplifies the low energy argument even in the classical case of $m=1$. Comment: 16 pages, revised. This paper extends the authors' work in arXiv:2107.09620 to capture endpoints in even dimensions. Updated according to referee comments, to appear in the J. of Differential Equations |
| Databáze: | arXiv |
| Externí odkaz: |
|