{"created":"2023-06-26T11:01:16.003574+00:00","id":1932,"links":{},"metadata":{"_buckets":{"deposit":"ea2efa8c-78ed-42d8-850c-df3a7c79c5e5"},"_deposit":{"created_by":30,"id":"1932","owners":[30],"pid":{"revision_id":0,"type":"depid","value":"1932"},"status":"published"},"_oai":{"id":"oai:oist.repo.nii.ac.jp:00001932","sets":["6:193"]},"author_link":["12689","12690"],"item_10001_biblio_info_7":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2020-11-30","bibliographicIssueDateType":"Issued"},"bibliographicPageStart":"2050072","bibliographic_titles":[{},{"bibliographic_title":"Communications in Contemporary Mathematics","bibliographic_titleLang":"en"}]}]},"item_10001_creator_3":{"attribute_name":"Author","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Spector, Daniel"}],"nameIdentifiers":[{}]},{"creatorNames":[{"creatorName":"Stockdale, Cody B."}],"nameIdentifiers":[{}]}]},"item_10001_description_5":{"attribute_name":"Abstract","attribute_value_mlt":[{"subitem_description":"Let Rj denote the jth Riesz transform on ℝn. We prove that there exists an absolute constant C>0 such that [Formula: see text] for any λ>0 and f∈L¹(ℝⁿ), where the above supremum is taken over measures of the form [Formula: see text]. This shows that to establish dimensional estimates for the weak-type (1,1) inequality for the Riesz transforms it suffices to study the corresponding weak-type inequality for Riesz transforms applied to a finite linear combination of Dirac masses. We use this fact to give a new proof of the best known dimensional upper bound, while our reduction result also applies to a more general class of Calderón–Zygmund operators.","subitem_description_type":"Other"}]},"item_10001_publisher_8":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_publisher":"World Scientific Publishing "}]},"item_10001_relation_14":{"attribute_name":"DOI","attribute_value_mlt":[{"subitem_relation_type":"isIdenticalTo","subitem_relation_type_id":{"subitem_relation_type_id_text":"info:doi/10.1142/S0219199720500728","subitem_relation_type_select":"DOI"}}]},"item_10001_relation_17":{"attribute_name":"Related site","attribute_value_mlt":[{"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://www.worldscientific.com/doi/10.1142/S0219199720500728","subitem_relation_type_select":"URI"}}]},"item_10001_rights_15":{"attribute_name":"Rights","attribute_value_mlt":[{"subitem_rights":"© 2020 The Author(s)."}]},"item_10001_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"0219-1997","subitem_source_identifier_type":"ISSN"},{"subitem_source_identifier":"1793-6683","subitem_source_identifier_type":"ISSN"}]},"item_10001_version_type_20":{"attribute_name":"Author's flag","attribute_value_mlt":[{"subitem_version_resource":"http://purl.org/coar/version/c_970fb48d4fbd8a85","subitem_version_type":"VoR"}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2021-02-15"}],"displaytype":"detail","filename":"s0219199720500728.pdf","filesize":[{"value":"299.2 kB"}],"format":"application/pdf","license_note":"Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (https://creativecommons.org/licenses/by-nc-nd/4.0/)","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"s0219199720500728","url":"https://oist.repo.nii.ac.jp/record/1932/files/s0219199720500728.pdf"},"version_id":"2fbe3400-6c54-4995-8bff-5e8c1d454ef6"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Riesz transforms","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"dimensional dependence","subitem_subject_language":"en","subitem_subject_scheme":"Other"},{"subitem_subject":"weak-type estimates","subitem_subject_language":"en","subitem_subject_scheme":"Other"}]},"item_language":{"attribute_name":"言語","attribute_value_mlt":[{"subitem_language":"eng"}]},"item_resource_type":{"attribute_name":"資源タイプ","attribute_value_mlt":[{"resourcetype":"journal article","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"On the dimensional weak-type (1,1) bound for Riesz transforms","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"On the dimensional weak-type (1,1) bound for Riesz transforms","subitem_title_language":"en"}]},"item_type_id":"10001","owner":"30","path":["193"],"pubdate":{"attribute_name":"公開日","attribute_value":"2021-02-15"},"publish_date":"2021-02-15","publish_status":"0","recid":"1932","relation_version_is_last":true,"title":["On the dimensional weak-type (1,1) bound for Riesz transforms"],"weko_creator_id":"30","weko_shared_id":30},"updated":"2023-06-26T11:40:08.125752+00:00"}