{"created":"2023-07-27T06:44:35.439320+00:00","id":34869,"links":{},"metadata":{"_buckets":{"deposit":"2e029aea-d173-4cba-8f21-03a84d9e1450"},"_deposit":{"created_by":3,"id":"34869","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34869"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034869","sets":["2812:2813:2835"]},"author_link":["88631","75"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"1999-03-01","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"4p.","bibliographicVolumeNumber":"1997-1998","bibliographic_titles":[{"bibliographic_title":"平成10(1998)年度 科学研究費補助金 基盤研究(C) 研究成果報告書"},{"bibliographic_title":"1998 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":"Marcinkiewicz積分を含むいくつかの一変数のLittlewood-Paley型のsquare functions間には点ごとの同値性が成立することが知られていて(G.Sunouchiの結果)いくつかの重要な応用が得られている.一方,調和解析の最近の発展によりマルチパラメーターsquare functionの重要性も広く認識されるようになった.本年度の研究により,上記の一変数のsquare functions間の点ごとの同値性がマルチパラメーターの場合に拡張された.また,これを利用していくつかのLittlewood-Paley型のsquare functionsのHp-Lp有界性、弱有界性が調べられた.ここでHpは直積空間上のハーディ空間,LpはLebesgue測度関してp乗可積分な可測関数のなす空間である.弱有界性を示す際、Stein-Nikishin-Maurey型の共鳴定理がオーリッツ空間に拡張され、利用された.この結果はLp空間上(1【less than or equal】p【less than or equa Littlewood-Paley理論における滑らかさの正則性のない積分核から定義されるsquare functionsに対しては,(Muckenhouptの)重みつきのLebesgue測度に関するLp空間上で,積分核のサイズに関するある条件のもとでそれらの有界な写像性が証明されているのであるが(前年度研究実績),重みのない通常のLp空間上では上記の積分核に関する条件を弱めることができることが示された.これは,1<p<2の場合と2【less than or equal】p<∞である場合とで異なったものとなり,前者に対してより強い条件となる.また,これらの条件は積分核のフーリエ変換の点ごとの評価を必要としないものであり,p=2の場合はさらに精密な結果が示されている.","subitem_description_type":"Abstract"},{"subitem_description":"(1)We proved the pointwise relations between some multiparameter square functions on R^n, and we applied them to prove H^p - L^p and L(log L)^<n-1> - L^<1, *> estimates for multiparameter Marcinkiewicz integrals. To show the weak type estimate, we also proved a resonance theorem on Orlicz spaces.\n(2)We proved that certain square function operators in the Littlewood-Paley theory defined by the kernels without any regularity are bounded on L^p_ 1 <p < *, w * A_p (the weights of Muckenhoupt). The kernels are satisfying only size and cancellation conditions. Then, we gave some applications to the Carleson measures on the upper half space.","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:09640168, 研究期間(年度):1997–1998","subitem_description_type":"Other"},{"subitem_description":"出典：「多変数コーリエ積分に関する基礎的・応用的研究」研究成果報告書　課題番号09640168\n  (KAKEN：科学研究費助成事業データベース（国立情報学研究所）)\n　　　本文データは著者版報告書より作成","subitem_description_type":"Other"}]},"item_9_identifier_registration":{"attribute_name":"ID登録","attribute_value_mlt":[{"subitem_identifier_reg_text":"10.24517/00034856","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-09640168/","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-09640168/096401681998kenkyu_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 1999-4p.pdf","filesize":[{"value":"162.1 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"ED-PR-SATO-S-kanen 1999-4p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/34869/files/ED-PR-SATO-S-kanen 1999-4p.pdf"},"version_id":"46276c7a-ea72-412f-a81b-03f46dc3836e"}]},"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":"多変数コ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":"多変数コ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":["2835"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34869","relation_version_is_last":true,"title":["多変数コ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":"2023-07-27T14:48:45.467917+00:00"}