{"created":"2023-07-27T06:44:30.101094+00:00","id":34748,"links":{},"metadata":{"_buckets":{"deposit":"ed38593c-85ec-45d3-aa4e-dbfb57438c22"},"_deposit":{"created_by":3,"id":"34748","owners":[3],"pid":{"revision_id":0,"type":"depid","value":"34748"},"status":"published"},"_oai":{"id":"oai:kanazawa-u.repo.nii.ac.jp:00034748","sets":["2812:2813:2827"]},"author_link":["88631","75"],"item_9_biblio_info_8":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2007-04-01","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"6p.","bibliographicVolumeNumber":"2005-2006","bibliographic_titles":[{"bibliographic_title":"平成18(2006)年度 科学研究費補助金 基盤研究(C) 研究成果報告書"},{"bibliographic_title":"2006 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":"滑らかさの正則性を持たない積分核から定義される、変化する回転面に沿ったCalderon-Zygmund型の特異積分に対して、ある種の積分核の大きさに関する条件のもとに、Lebesgue空間Lpでの有界性が示された.これにより、特に、2次元の場合に、Grafakos-Stefanovの斉次特異積分に対する結果がR.Fefferman型の非斉次特異積分の場合に拡張された.この結果が高次元の場合に拡張するかどうかはこれからの研究課題のひとつである(A note on the singular integrals associated with a variable surface of revolution, Dashan Fan and Shuichi Sato). 滑らかさの正則性を持たない積分核から定義されるCalderon-Zygmund型の特異積分に対してある種の積分核の大きさに関する条件のもとに、Lebesgue空間Lpでの精密なノルム評価が得られた。積分核のLq可積分性でqが1に近づく時の特異積分作用素の精密なLp評価を証明することにより、補外法(extrapolation)が適用できることになる。これにより、積分核の最小の大きさを仮定するだけで、特異積分作用素のLp,有界性が証明された。この結果はさらにRadon特異積分作用素の場合に拡張された。A.Al-Salman and Y.Panは論文Singular integrals with rough kernels in $Llog L(S^{n-1})$において少し違った方法で同様の結果を示している。我々の方法は積分核の大きさに対応した予想される最良のLpノルム評価を証明することにより、補外法の応用を可能とするものであり、新しい証明方法である。さらに、この方法によりA.Al-Salman and Y.Panの結果を一部改良することができた(Estimates for singular integrals and extrapolation)。","subitem_description_type":"Abstract"},{"subitem_description":"(1) We consider certain non-regular pseudo-differential operators T_σ and study the question of their boundedness on the weighted Triebel-Lizorkin and Besov spaces. In particular, we substantially relax the regularity condition on the symbol σ due to Bourdaud for T to be bounded on the Sobolev spaces H^s_p.\n(2) We prove the Lp boundedness of the singular integral operators associated with a variable surface of revolution assuming the boundedness of related lower dimensional maximal operators. The singular integrals are defined by rough kernels satisfying certain size and cancellation conditions. As an application, we extend a result of Grafakos-Stefanov and Fan-Guo-Pan to the case of a singular integral of R. Fefferman type of two variables.\n(3) We study singular integrals with rough kernels, which belong to a class of singular Radon transforms. We prove certain estimates for the singular integrals that are useful in an extrapolation argument. As an application, we prove Lp boundedness of the singular integrals under a certain sharp size condition on their kernels.\n(4) We prove certain Lp estimates (1<p<∞) for non-isotropic singular integrals along surfaces of revolution. The singular integrals are defined by rough kernels with generalized homogeneity. As an application we obtain Lp boundedness of the singular integrals under a sharp size condition on their kernels. We also prove a certain estimate for a trigonometric integral, which is useful in studying non-isotropic singular integrals and implies the Stein-Wainger estimate for a trigonometric integral involving a phase function defined by a curve that does not lie in an affine hyperplane.\n(5) We consider a singular integral along a manifold of finite type. We prove a sharp Lp estimate for the singular integral operator according to a size condition of its kernel, which is useful in applying an extrapolation method.","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:17540154, 研究期間(年度):2005–2006","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17540154\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":"10.24517/00034735","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-17540154/","subitem_relation_type_select":"URI"}},{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-17540154/175401542006kenkyu_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 2007-6p.pdf","filesize":[{"value":"238.7 kB"}],"format":"application/pdf","licensetype":"license_11","mimetype":"application/pdf","url":{"label":"ED-PR-SATO-S-kanen 2007-6p.pdf","url":"https://kanazawa-u.repo.nii.ac.jp/record/34748/files/ED-PR-SATO-S-kanen 2007-6p.pdf"},"version_id":"8d0840c3-5b25-4100-8213-3118ac6b50cd"}]},"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":["2827"],"pubdate":{"attribute_name":"公開日","attribute_value":"2017-10-05"},"publish_date":"2017-10-05","publish_status":"0","recid":"34748","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":"2023-07-27T14:34:46.812679+00:00"}