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The $L^p$ boundedness of wave operators for Schr\""odinger operators with threshold singularities II. Even dimensional case
http://hdl.handle.net/2261/8113
http://hdl.handle.net/2261/81132776fe91-7e6d-4f47-b408-c1984068f3a0
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms130302.pdf (481.9 kB)
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| Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||
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| 公開日 | 2008-03-04 | |||||
| タイトル | ||||||
| タイトル | The $L^p$ boundedness of wave operators for Schr\""odinger operators with threshold singularities II. Even dimensional case | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_6501 | |||||
| タイプ | departmental bulletin paper | |||||
| 著者 |
Finco, Domenico
× Finco, Domenico× Yajima, Kenji |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | Let $H_0=-\lap$ and $H=-\lap +V(x)$ be Schr\""odinger operators on $\R^m$ and $m \geq 6$ be even. We assume that $\Fg(\ax^{-2\s}V) \in L^{m_\ast}(\R^m)$ for some $\s>\frac{1}{m_\ast}$, $m_\ast=\frac{m-1}{m-2}$ and $ | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | V(x) | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | \leq C \ax^{-\d}$ for some $\d>m+2$, so that the wave operators $W_\pm=\lim_{t\to \pm \infty} e^{itH}e^{-itH_0}$ exist. We show the following mapping properties of $W_\pm$: (1) If $0$ is not an eigenvalue of $H$, $W_\pm$ are bounded in Sobolev spaces $W^{k,p}(\R^m)$ for all $0 \leq k \leq 2$ and $1<p<\infty$ and also in $L^1(\R^m)$ and $L^\infty(\R^m)$; (2) if $0$ is an eigenvalue of $H$ and if $V$ satisfies stronger decay condition $ | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | V(x) | |||||
| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | \leq C\ax^{-\d}$, $\d>m+4$ if $m=6$ and $\d>m+3$ if $m\geq 8$, $W_\pm$ are bounded in $W^{k,p}(\R^m)$ for all $0 \leq k \leq 2$ and $\frac{m}{m-2}<p<\frac{m}2$; (3) the same holds in Sobolev spaces of higher orders if derivatives of $V(x)$ satisfy suitable boundedness conditions. This paper is a continuation of the one with the same title, part one, where odd dimensional cases $m \geq 3$ are treated, however, it can mostly be read independently. | |||||
| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 13, 号 3, p. 277-346, 発行日 2006-12-27 |
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| ISSN | ||||||
| 収録物識別子タイプ | ISSN | |||||
| 収録物識別子 | 13405705 | |||||
| 書誌レコードID | ||||||
| 収録物識別子タイプ | NCID | |||||
| 収録物識別子 | AA11021653 | |||||
| フォーマット | ||||||
| 内容記述タイプ | Other | |||||
| 内容記述 | application/pdf | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 415 | |||||
| Mathematical Reviews Number | ||||||
| MR2284405 | ||||||
| Mathmatical Subject Classification | ||||||
| 57M50(MSC2000) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 2005-08-11 | ||||||
