{"_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"}, "item_4_biblio_info_7": {"attribute_name": "\u66f8\u8a8c\u60c5\u5831", "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": "\u30d5\u30a9\u30fc\u30de\u30c3\u30c8", "attribute_value_mlt": [{"subitem_description": "application/pdf", "subitem_description_type": "Other"}]}, "item_4_description_5": {"attribute_name": "\u6284\u9332", "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 $\\s\u003e\\frac{1}{m_\\ast}$, $m_\\ast=\\frac{m-1}{m-2}$ and  $", "subitem_description_type": "Abstract"}, {"subitem_description": "V(x)", "subitem_description_type": "Abstract"}, {"subitem_description": "\\leq C \\ax^{-\\d}$ for some $\\d\u003em+2$, 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 $1\u003cp\u003c\\infty$ 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 $", "subitem_description_type": "Abstract"}, {"subitem_description": "V(x)", "subitem_description_type": "Abstract"}, {"subitem_description": "\\leq C\\ax^{-\\d}$, $\\d\u003em+4$ if $m=6$  and $\\d\u003em+3$ if $m\\geq 8$, $W_\\pm$ are bounded in $W^{k,p}(\\R^m)$ for all  $0 \\leq k \\leq 2$ and $\\frac{m}{m-2}\u003cp\u003c\\frac{m}2$; (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": "\u51fa\u7248\u8005", "attribute_value_mlt": [{"subitem_publisher": "Graduate School of Mathematical Sciences, The University of Tokyo"}]}, "item_4_source_id_10": {"attribute_name": "\u66f8\u8a8c\u30ec\u30b3\u30fc\u30c9ID", "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": "\u65e5\u672c\u5341\u9032\u5206\u985e\u6cd5", "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": "\u539f\u7a3f\u53d7\u9818\u65e5", "attribute_value_mlt": [{"subitem_text_value": "2005-08-11"}]}, "item_4_text_34": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "attribute_value_mlt": [{"subitem_text_value": "Departmental Bulletin Paper"}]}, "item_creator": {"attribute_name": "\u8457\u8005", "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": "\u30d5\u30a1\u30a4\u30eb\u60c5\u5831", "attribute_type": "file", "attribute_value_mlt": [{"accessrole": "open_date", "date": [{"dateType": "Available", "dateValue": "2017-06-27"}], "displaytype": "detail", "download_preview_message": "", "file_order": 0, "filename": "jms130302.pdf", "filesize": [{"value": "481.9 kB"}], "format": "application/pdf", "future_date_message": "", "is_thumbnail": false, "licensetype": "license_free", "mimetype": "application/pdf", "size": 481900.0, "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": "\u8a00\u8a9e", "attribute_value_mlt": [{"subitem_language": "eng"}]}, "item_resource_type": {"attribute_name": "\u8cc7\u6e90\u30bf\u30a4\u30d7", "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": "\u30bf\u30a4\u30c8\u30eb", "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": ["312/6865/6959/6960", "9/504/6868/6961/6962"], "permalink_uri": "http://hdl.handle.net/2261/8113", "pubdate": {"attribute_name": "\u516c\u958b\u65e5", "attribute_value": "2008-03-04"}, "publish_date": "2008-03-04", "publish_status": "0", "recid": "40114", "relation": {}, "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_shared_id": null}