{"created":"2021-03-01T06:59:41.496691+00:00","id":40114,"links":{},"metadata":{"_buckets":{"deposit":"9bc8cd54-c0fc-4bdc-b2b5-dfa69d42f2b3"},"_deposit":{"id":"40114","owners":[],"pid":{"revision_id":0,"type":"depid","value":"40114"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00040114","sets":["312:6865:6959:6960","9:504:6868:6961:6962"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2006-12-27","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"3","bibliographicPageEnd":"346","bibliographicPageStart":"277","bibliographicVolumeNumber":"13","bibliographic_titles":[{"bibliographic_title":"Journal of mathematical sciences, the University of Tokyo"}]}]},"item_4_description_13":{"attribute_name":"フォーマット","attribute_value_mlt":[{"subitem_description":"application/pdf","subitem_description_type":"Other"}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"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  $","subitem_description_type":"Abstract"},{"subitem_description":"V(x)","subitem_description_type":"Abstract"},{"subitem_description":"\\leq C \\ax^{-\\d}$ 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 $","subitem_description_type":"Abstract"},{"subitem_description":"V(x)","subitem_description_type":"Abstract"},{"subitem_description":"\\leq C\\ax^{-\\d}$, $\\d>m+4$ 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.","subitem_description_type":"Abstract"}]},"item_4_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Mathematical Sciences, The University of Tokyo"}]},"item_4_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11021653","subitem_source_identifier_type":"NCID"}]},"item_4_source_id_8":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"13405705","subitem_source_identifier_type":"ISSN"}]},"item_4_subject_15":{"attribute_name":"日本十進分類法","attribute_value_mlt":[{"subitem_subject":"415","subitem_subject_scheme":"NDC"}]},"item_4_text_16":{"attribute_name":"Mathematical Reviews Number","attribute_value_mlt":[{"subitem_text_value":"MR2284405"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"57M50(MSC2000)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"2005-08-11"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Finco, Domenico"}],"nameIdentifiers":[{"nameIdentifier":"138690","nameIdentifierScheme":"WEKO"}]},{"creatorNames":[{"creatorName":"Yajima, Kenji"}],"nameIdentifiers":[{"nameIdentifier":"138691","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-06-27"}],"displaytype":"detail","filename":"jms130302.pdf","filesize":[{"value":"481.9 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms130302.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/40114/files/jms130302.pdf"},"version_id":"ec511602-add0-4910-9f47-cd6bba21b6e7"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"The $L^p$ boundedness of wave operators for Schr\\\"\"odinger operators with threshold singularities II. Even dimensional case","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"The $L^p$ boundedness of wave operators for Schr\\\"\"odinger operators with threshold singularities II. Even dimensional case"}]},"item_type_id":"4","owner":"1","path":["6960","6962"],"pubdate":{"attribute_name":"公開日","attribute_value":"2008-03-04"},"publish_date":"2008-03-04","publish_status":"0","recid":"40114","relation_version_is_last":true,"title":["The $L^p$ boundedness of wave operators for Schr\\\"\"odinger operators with threshold singularities II. Even dimensional case"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:13:31.997277+00:00"}