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The $W^{k,p}$-continuity of wave operators for Schrödinger operators III, even dimensional cases $m\geq4$
http://hdl.handle.net/2261/1560
http://hdl.handle.net/2261/1560af1c5030-93ec-47e4-8b46-544ec34d1434
| 名前 / ファイル | ライセンス | アクション |
|---|---|---|
jms020204.pdf (290.9 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 $W^{k,p}$-continuity of wave operators for Schrödinger operators III, even dimensional cases $m\geq4$ | |||||
| 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 |
Yajima, Kenji
× Yajima, Kenji |
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| 抄録 | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | Let $H=-Δ+V(x)$ be the Schrodinger operator on ${\bf R}^m$, $m\ge 3$. We show that the wave operators $W_\pm=\lim_{t\to\pm\infty}e^{itH}\cdot e^{-itH_0}$, $H_0=-Δ$, are bounded in Sobolev spaces $W^{k, p}({\bf R}^m)$, $1\le p\le\infty$, $k=0, 1, \ldots, \ell$, if $V$ satisfies $\|D^α V(y)\|_{L^{p_0}(|x-y|\le 1)}\le C(1+|x|)^{-δ}$ for $δ>(3m/2)+1$, $p_0>m/2$ and $|α|\le\ell+\ell_0$, where $\ell_0=0$ if $m=3$ and $\ell_0=[(m-1)/2]$ if $m\ge 4$, $[σ]$ is the integral part of $σ$. This result generalizes the author's previous result which appears in J. Math.\ Soc.\ Japan 47, where the theorem is proved for the odd dimensional cases $m\ge 3$ and several applications such as $L^p$-decay of solutions of the Cauchy problems for time-dependent Schrodinger equations and wave equations with potentials, and the $L^p$-boundedness of Fourier multiplier in generalized eigenfunction expansions are given. | |||||
| 書誌情報 |
Journal of mathematical sciences, the University of Tokyo 巻 2, 号 2, p. 311-346, 発行日 1995 |
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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 | ||||||
| MR1366561 | ||||||
| Mathmatical Subject Classification | ||||||
| 47A40(MSC1991) | ||||||
| Mathmatical Subject Classification | ||||||
| 35P25(MSC1991) | ||||||
| Mathmatical Subject Classification | ||||||
| 81Uxx(MSC1991) | ||||||
| 出版者 | ||||||
| 出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| 原稿受領日 | ||||||
| 1994-09-19 | ||||||
