A note on endpoint $L^p$-continuity of wave operators for classical and higher order Schrödinger operators
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866909533024026624 |
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| author | Erdogan, M. Burak Green, William R. |
| author_facet | Erdogan, M. Burak Green, William R. |
| contents | We consider the higher order Schrödinger operator $H=(-Δ)^m+V(x)$ 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 $m=1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_14264 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A note on endpoint $L^p$-continuity of wave operators for classical and higher order Schrödinger operators Erdogan, M. Burak Green, William R. Analysis of PDEs We consider the higher order Schrödinger operator $H=(-Δ)^m+V(x)$ 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 $m=1$. |
| title | A note on endpoint $L^p$-continuity of wave operators for classical and higher order Schrödinger operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2207.14264 |