{"created":"2023-07-27T06:44:32.885085+00:00","id":34811,"links":{},"metadata":{"_buckets":{"deposit":"85be651d-8e9b-49a9-ba35-1b1f1bb98928"},"_deposit":{"created_by":3,"id":"34811","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34811"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034811","sets":["2812:2813:2831"]},"author_link":["69921","75"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2003-04-01","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"5p.","bibliographicVolumeNumber":"2001-2002","bibliographic_titles":[{"bibliographic_title":"平成14(2002)年度 科学研究費補助金 基盤研究(C) 研究成果報告書"},{"bibliographic_title":"2002 Fiscal Year Final Research Report","bibliographic_titleLang":"en"}]}]},"item_9_creator_33":{"attribute_name":"著者別表示","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{}],"nameIdentifiers":[{},{}]}]},"item_9_description_21":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"(1)滑らかさの正則性のない積分核から定義されるCalderon-Zygmund型の特異積分とLittlewood-Paley関数に対してウェートつきの弱(1,1)評価が得られた。(2)ある種のLittlewood-Paley関数に対して,ウェートつきのHardy空間上での弱・強評価が得られた。さらに一般化されたBochner-Riesz作用素,球面平均作用素に対するいくつかのウェートつきの評価とその応用が得られた。(3)ある種の擬微分作用素のウェートつきのL^2有界性,H^1-L^1有界性に対して表象の満たすべき滑らかさの正則性に関する条件が改良された。(4)変化する回転面に付随した特異積分のL^P有界性を示した.この場合特異積分の積分核の斉次部分にはH^1条件とcancellation条件を仮定する.また,この特異積分に付随したある種のmaximal functionのL^q有界性も仮定されている。(5)滑らかさの正則性のない積分核から定義されるある種の多重線形Littlewood-Paley作用素のL^P有界性を示した.この応用として,より広範の多重線形Fourier multiplier作用素のL^P有界性が示される事になった。(6)積分核に単位球面上でLlog L条件を仮定すると,これにより定義されるMarcinkiewicz関数がweak(1,1)評価を満足することを示した。(7)n次元Euclid空間とトーラス上のL^P空間,Hardy空間に作用する多重線形作用素間のトランスファランス定理とその応用が示された.(8)n次元Euclid空間とトーラス上のLittlewood-Paley関数のL^p評価,弱L^p評価,H^p-L^p評価,H^P-弱L^P評価等の評価間のトランスファランス定理とその応用が示された。(9)滑らかさの正則性のない積分核から定義される,回転面に付随した特異積分とLittlewood-Paley関数が研究された.","subitem_description_type":"Abstract"},{"subitem_description":"(1) We proved the weighted weak type (1,1) estimates both for the Calderon-Zygmund type singular integrals and for the Littlewood-Paley functions. These operators are defined by certain rough kernels.\n(2) We proved some weighted estimates for the Littlewood-Paley functions on the weighted Hardy spaces. Also some weighted estimates for the generalized Bochner-Riesz operators and for the generalized spherical means are obtained.\n(3) For certain classes of pseudo-differential operators, we proved L^2_w - L^2_w, L^1_w - L^<1,∽>_w and H^1_w - L^1_w estimates.\n(4) We proved the L^p estimates for certain singular integrals associated to the variable surface of revolution.\n(5) We studied certain multilinear Littlewood-Paley functions arising from rough kernels.\n(6) We proved the weak type (1,1) estimates for the Marcinkiewicz integrals by assuming for the kernel the LlogL condition on the unit sphere S^<n-1>.\n(7) We proved transference theorems between the multilinear multiplier operators on the Euclid space R^n and the ones on the torus T^n. Also we obtained some applications of these results.\n(8) We proved transference theorems for the L^p, the weak L^p and H^p - L^p estimates between the Littlewood-Paley functions on the Euclid space R^n and those on the torus T^n. Also we obtained some applications of these results.\n(9) We proved the L^p estimates for the Littlewood-Paley functions along curves and the related singular integrals, both arising from the rough kernels. As applications, we proved the L^p estimates for the Marcinkiewicz integrals along curves and the singular integrals associated to the surface of revolution, both with H^1 kernels.","subitem_description_type":"Abstract"}]},"item_9_description_22":{"attribute_name":"内容記述","attribute_value_mlt":[{"subitem_description":"研究課題/領域番号:13640159, 研究期間(年度):2001–2002","subitem_description_type":"Other"}]},"item_9_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24517/00034798","subitem_identifier_reg_type":"JaLC"}]},"item_9_publisher_17":{"attribute_name":"公開者","attribute_value_mlt":[{"subitem_publisher":"金沢大学教育学部"}]},"item_9_relation_28":{"attribute_name":"関連URI","attribute_value_mlt":[{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/search/?qm=20162430","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640159/","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-13640159/136401592002kenkyu_seika_hokoku_gaiyo/","subitem_relation_type_select":"URI"}}]},"item_9_version_type_25":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_ab4af688f83e57aa","subitem_version_type":"AM"}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2017-10-05"}],"displaytype":"detail","filename":"ED-PR-SATO-S-kanen 2003-5p.pdf","filesize":[{"value":"177.2 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"ED-PR-SATO-S-kanen 2003-5p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/34811/files/ED-PR-SATO-S-kanen 2003-5p.pdf"},"version_id":"6a04151e-da31-4467-98b5-7d21d61c7e38"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"jpn"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"research report","resourceuri":"http://purl.org/coar/resource_type/c_18ws"}]},"item_title":"多変数フーリエ積分に関する基礎的・応用的研究","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"多変数フーリエ積分に関する基礎的・応用的研究"},{"subitem_title":"Research on Fourier integrals of several variables","subitem_title_language":"en"}]},"item_type_id":"9","owner":"3","path":["2831"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34811","relation_version_is_last":true,"title":["多変数フーリエ積分に関する基礎的・応用的研究"],"weko_creator_id":"3","weko_shared_id":3},"updated":"2023-07-27T14:41:27.901529+00:00"}