Characterization of infinitesimal boundedness of Schrödinger operator
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909572719968256 |
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| author | Chen, Yanhan |
| author_facet | Chen, Yanhan |
| contents | In this paper, we characterize the weighted infinitesimal boundedness: for $0<α<n$ and $1<p<\infty$,
$$\|Vϕ\|_{L^{p}(w)}^{p}\leqε\|(-Δ)^{\fracα{2}}ϕ\|_{L^{p}(w)}^{p}+C(ε)\|ϕ\|_{L^{p}(w)}^{p}.$$
In particular, we extend the classical result due to Maz'ya and Verbitsky by using Carleson condition, localization estimates and capacity theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_06765 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Characterization of infinitesimal boundedness of Schrödinger operator Chen, Yanhan Classical Analysis and ODEs 47A55, 31B15, 47D08 In this paper, we characterize the weighted infinitesimal boundedness: for $0<α<n$ and $1<p<\infty$, $$\|Vϕ\|_{L^{p}(w)}^{p}\leqε\|(-Δ)^{\fracα{2}}ϕ\|_{L^{p}(w)}^{p}+C(ε)\|ϕ\|_{L^{p}(w)}^{p}.$$ In particular, we extend the classical result due to Maz'ya and Verbitsky by using Carleson condition, localization estimates and capacity theory. |
| title | Characterization of infinitesimal boundedness of Schrödinger operator |
| topic | Classical Analysis and ODEs 47A55, 31B15, 47D08 |
| url | https://arxiv.org/abs/2504.06765 |