{"created":"2023-07-27T06:44:31.250927+00:00","id":34774,"links":{},"metadata":{"_buckets":{"deposit":"4aecb710-41a6-4bdb-9acc-394a6543377e"},"_deposit":{"created_by":3,"id":"34774","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34774"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034774","sets":["2812:2813:2829"]},"author_link":["85759","75"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2005-04-01","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"5p.","bibliographicVolumeNumber":"2003-2004","bibliographic_titles":[{"bibliographic_title":"平成16(2004)年度 科学研究費補助金 基盤研究(C) 研究成果報告書"},{"bibliographic_title":"2004 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)Weighted estimates for the maximal functions associated with Fourier multipliers by Shuichi Sato 内容の概略. Bochner-Riesz型のある種のFourier multiplierから定義される最大関数に対していくつかの加重不等式が証明された.次のような一般化されたBochner-Riesz平均S^{lambda}_t(f)を考える.通常のBochner-Riesz平均から定義される最大関数に対するいくつかの既知の加重不等式をこの一般化されたBochner-Riesz平均から定義される最大関数$S^lambda_*$の場合に拡張した.特に,最大関数$S^lambda_*$対する加重不等式を$gamma(t,xi)=t^{-1}|Phi(xi)|$, $gamma(t,xi)=|Phi(t^{-1}xi)|$の場合に証明した.ここで$Phi$は$Bbb R^n$から$Bbb R^n$への写像である種の正則性を満足するものである.$h$が$Bbb R^n$上の正の1次斉次関数で,原点を除いて無限回微分可能ならば,適当な$Phi$をとると$|Phi(xi)|=h(xi)$とできることが知られている. (2)Non-regular pseudo-differential operators on the weighted Triebel-Lizorkin spaces by Shuichi Sato 内容の概略. ある種の擬微分作用素$T_sigma$を考え,その加重Triebel-Lizorkin空間,加重Besov空間上での有界性を調べた.特に,Sobolev空間$H^s_p$($pgeq 2$)上で$T_sigma$が有界になるためのBourdaudによる$sigma$の正則性に関する条件が本質的に改良された.","subitem_description_type":"Abstract"},{"subitem_description":"(1)We proved the weighted weak type (1,1) estimates for the Calderon-Zygmund type singular integrals. These operators are defined by certain rough kernels. We assume that the kernel satisfies a certain size condition and a cancellation condition along with a Dini type condition. These results are a generalization to R^n, n【greater than or equal】3, of the results of A. Vargas on the weak (1,1) estimates for the singular integrals with homogeneous kernels. Also, they are a generalization to the case of inhomogeneous kernels on R^n, n【greater than or equal】2, of the results of A. Vargas. The weighted weak type estimates for the Littlewood-Paley functions are also shown by assuming analogous conditions for the kernels.\n(2)For certain classes of pseudo-differential operators, we proved L^2_ω-L^2_ω, L^1_ω-L^<1,∞>_ω and H^1_ω-L^1_ω estimates. We proved L^2_ω-L^2_ωestimates for a pseudo-differential operators with a symbol satisfying a minimal regularity condition, where the weight ω is in A_1 of Muckenhoupt weight class. This improves a result of K. Yabuta. The L^1_ω-L^<1,∞>_ω and H^1_ω-L^1_ω estimates were proved by applying Carbery's method.\n(3)We studied the singular integrals associated with the variable surfaces of revolution. We treated the rough kernel case where the singular integral is defined by an H^1 kernel function on the sphere S^<n-1>. We proved the L^p boundedness of the singular integral for 1<p【less than or equal】2 assuming that a certain lower dimensional maximal operator is bounded on L^s for all s>1. We also studied the (L^p, L^r) boundedness for the fractional integrals associated with the surfaces of revolution.\n(4)We proved some weighted estimates for the maximal functions associated with certain Fourier multipliers of Bochner-Riesz type.\n(5)We considered certain non-regular pseudo-differential operators T_σ and studied the question of their boundedness on the weighted Triebel-Lizorkin and Besov spaces. In particular, we substantially relaxed the regularity condition on the symbol σ due to Bourdaud for T_σ to be bounded on the Sobolev spaces H^s_p (p【greater than or equal】2).","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:15540160, 研究期間(年度):2003–2004","subitem_description_type":"Other"},{"subitem_description":"出典：「多変数フ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15540160\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_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-15540160/","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-15540160/155401602004kenkyu_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 2005-5p.pdf","filesize":[{"value":"166.7 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"ED-PR-SATO-S-kanen 2005-5p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/34774/files/ED-PR-SATO-S-kanen 2005-5p.pdf"},"version_id":"a059be04-72b8-4d35-92d9-703f5bf2374f"}]},"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":["2829"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34774","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":"2023-07-27T14:29:36.951031+00:00"}