The $L^p$-continuity of wave operators for fractional order Schrödinger operators
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866914051210084352 |
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| author | Erdogan, M. Burak Goldberg, Michael Green, William |
| author_facet | Erdogan, M. Burak Goldberg, Michael Green, William |
| contents | We consider fractional Schrödinger operators $H=(-Δ)^α+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2α$, $α>1$. We show that the wave operators extend to bounded operators on $L^p(\mathbb R^n)$ for all $1\leq p\leq\infty$ under conditions on the potential that depend on $n$ and $α$ analogously to the case when $α\in \mathbb N$. As a consequence, we deduce a family of dispersive and Strichartz estimates for the perturbed fractional Schrödinger operator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_18003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The $L^p$-continuity of wave operators for fractional order Schrödinger operators Erdogan, M. Burak Goldberg, Michael Green, William Analysis of PDEs We consider fractional Schrödinger operators $H=(-Δ)^α+V(x)$ in $n$ dimensions with real-valued potential $V$ when $n>2α$, $α>1$. We show that the wave operators extend to bounded operators on $L^p(\mathbb R^n)$ for all $1\leq p\leq\infty$ under conditions on the potential that depend on $n$ and $α$ analogously to the case when $α\in \mathbb N$. As a consequence, we deduce a family of dispersive and Strichartz estimates for the perturbed fractional Schrödinger operator. |
| title | The $L^p$-continuity of wave operators for fractional order Schrödinger operators |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2509.18003 |