{"created":"2023-06-26T11:00:57.946962+00:00","id":1561,"links":{},"metadata":{"_buckets":{"deposit":"a9c322c6-f1d9-4ff3-87d9-739006511405"},"_deposit":{"created_by":29,"id":"1561","owners":[29],"pid":{"revision_id":0,"type":"depid","value":"1561"},"status":"published"},"_oai":{"id":"oai:oist.repo.nii.ac.jp:00001561","sets":["6:193"]},"author_link":["9429"],"item_10001_biblio_info_7":{"attribute_name":"Bibliographic Information","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2020-02-13","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"2","bibliographicPageEnd":"168","bibliographicPageStart":"153","bibliographicVolumeNumber":"76","bibliographic_titles":[{},{"bibliographic_title":"Portugaliae Mathematica","bibliographic_titleLang":"en"}]}]},"item_10001_creator_3":{"attribute_name":"Author","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Spector, Daniel"}],"nameIdentifiers":[{}]}]},"item_10001_description_5":{"attribute_name":"Abstract","attribute_value_mlt":[{"subitem_description":"In this paper we give a streamlined proof of an inequality recently obtained by the author: For every α∈(0,1) there exists a constant C=C(α,d)>0 such that\n [Formula: see text]\nfor all u∈Lq(Rd) for some 1≤q<d/(1−α) such that Dαu:=∇I1−αu∈L1(Rd;Rd). We also give a counterexample which shows that in contrast to the case α=1, the fractional gradient does not admit an L1 trace inequality, i.e.  [Formula: see text] cannot control the integral of u with respect to the Hausdorff content  [Formula: see text]. The main substance of this counterexample is a result of interest in its own right, that even a weak-type estimate for the Riesz transforms fails on the space  [Formula: see text], β∈[1,d). It is an open question whether this failure of a weak-type estimate for the Riesz transforms extends to β∈(0,1). ","subitem_description_type":"Other"}]},"item_10001_publisher_8":{"attribute_name":"Publisher","attribute_value_mlt":[{"subitem_publisher":"European Mathematical Society"}]},"item_10001_relation_14":{"attribute_name":"DOI","attribute_value_mlt":[{"subitem_relation_type_id":{"subitem_relation_type_id_text":"info:doi/10.4171/PM/2031","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.ems-ph.org/journals/show_abstract.php?issn=0032-5155&vol=76&iss=2&rank=4","subitem_relation_type_select":"URI"}},{"subitem_relation_name":[{"subitem_relation_name_text":"arXiv.org"}],"subitem_relation_type_id":{"subitem_relation_type_id_text":"https://arxiv.org/abs/1906.05541","subitem_relation_type_select":"URI"}}]},"item_10001_rights_15":{"attribute_name":"Rights","attribute_value_mlt":[{"subitem_rights":"© 2020 EMS Publishing House."}]},"item_10001_source_id_9":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"0032-5155","subitem_source_identifier_type":"ISSN"},{"subitem_source_identifier":"1662-2758","subitem_source_identifier_type":"ISSN"}]},"item_access_right":{"attribute_name":"アクセス権","attribute_value_mlt":[{"subitem_access_right":"metadata only access","subitem_access_right_uri":"http://purl.org/coar/access_right/c_14cb"}]},"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":"A noninequality for the fractional gradient","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"A noninequality for the fractional gradient","subitem_title_language":"en"}]},"item_type_id":"10001","owner":"29","path":["193"],"pubdate":{"attribute_name":"公開日","attribute_value":"2020-06-22"},"publish_date":"2020-06-22","publish_status":"0","recid":"1561","relation_version_is_last":true,"title":["A noninequality for the fractional gradient"],"weko_creator_id":"29","weko_shared_id":29},"updated":"2023-06-26T11:47:38.050021+00:00"}