{"created":"2021-03-01T07:10:06.552793+00:00","id":49244,"links":{},"metadata":{"_buckets":{"deposit":"376f6a0d-56fa-4f18-a84b-d84cf7f6fb05"},"_deposit":{"id":"49244","owners":[],"pid":{"revision_id":0,"type":"depid","value":"49244"},"status":"published"},"_oai":{"id":"oai:repository.dl.itc.u-tokyo.ac.jp:00049244","sets":["312:6865:6866:7722","9:504:6868:6869:7725"]},"item_4_biblio_info_7":{"attribute_name":"書誌情報","attribute_value_mlt":[{"bibliographicIssueDates":{"bibliographicIssueDate":"2016-10-31","bibliographicIssueDateType":"Issued"},"bibliographicIssueNumber":"4","bibliographicPageEnd":"740","bibliographicPageStart":"727","bibliographicVolumeNumber":"23","bibliographic_titles":[{"bibliographic_title":"Journal of Mathematical Sciences, The University of Tokyo"}]}]},"item_4_description_5":{"attribute_name":"抄録","attribute_value_mlt":[{"subitem_description":"For a Lebesgue integrable complex-valued function $f$ defined over the $m$-dimensional torus $\\mathbb {I}^m:=[0,1)^m$, let $\\hat f({\\bf n})$ denote the multiple Walsh-Fourier coefficient of $f$, where ${\\bf n}=\\left(n^{(1)},\\dots,n^{(m)}\\right)\\in (\\mathbb {Z}^+)^m$, $\\mathbb {Z^+}=\\mathbb {N}\\cup \\{0\\}$. The Riemann-Lebesgue lemma shows that $\\hat f({\\bf n})=o(1)$ as $|{\\bf n}|\\to \\infty$ for any $f\\in {\\rm L}^1(\\mathbb I^m)$.  However, it is known that, these Fourier coefficients can tend to zero as slowly as we wish.  The definitive result is due to Ghodadra Bhikha Lila for functions of bounded $p$-variation.  We shall prove that this is just a matter only of local bounded $p$-variation for functions with multiple Walsh-Fourier series lacunary with small gaps.  Our results, as in the case of trigonometric For a Lebesgue integrable complex-valued function $f$ defined over the $m$-dimensional torus $\\mathbb {I}^m:=[0,1)^m$, let $\\hat f({\\bf n})$ denote the multiple Walsh-Fourier coefficient of $f$, where ${\\bf n}=\\left(n^{(1)},\\dots,n^{(m)}\\right)\\in (\\mathbb {Z}^+)^m$, $\\mathbb {Z^+}=\\mathbb {N}\\cup \\{0\\}$. The Riemann-Lebesgue lemma shows that $\\hat f({\\bf n})=o(1)$ as $|{\\bf n}|\\to \\infty$ for any $f\\in {\\rm L}^1(\\mathbb I^m)$.  However, it is known that, these Fourier coefficients can tend to zero as slowly as we wish.  The definitive result is due to Ghodadra Bhikha Lila for functions of bounded $p$-variation.  We shall prove that this is just a matter only of local bounded $p$-variation for functions with multiple Walsh-Fourier series lacunary with small gaps.  Our results, as in the case of trigonometric Fourier series due to J.R. Patadia and R.G. Vyas, illustrate the interconnection between `localness' of the hypothesis and `type of lacunarity' and allow us to interpolate the results.","subitem_description_type":"Abstract"}]},"item_4_publisher_20":{"attribute_name":"出版者","attribute_value_mlt":[{"subitem_publisher":"Graduate School of Mathematical Sciences, The University of Tokyo"}]},"item_4_select_14":{"attribute_name":"著者版フラグ","attribute_value_mlt":[{"subitem_select_item":"publisher"}]},"item_4_source_id_10":{"attribute_name":"書誌レコードID","attribute_value_mlt":[{"subitem_source_identifier":"AA11021653","subitem_source_identifier_type":"NCID"}]},"item_4_source_id_8":{"attribute_name":"ISSN","attribute_value_mlt":[{"subitem_source_identifier":"13405705","subitem_source_identifier_type":"ISSN"}]},"item_4_text_17":{"attribute_name":"Mathmatical Subject Classification","attribute_value_mlt":[{"subitem_text_value":"42C10(MSC2010)"},{"subitem_text_value":"42B05(MSC2010)"},{"subitem_text_value":"26B30(MSC2010)"},{"subitem_text_value":" 26D15(MSC2010)"}]},"item_4_text_33":{"attribute_name":"原稿受領日","attribute_value_mlt":[{"subitem_text_value":"2014-11-17"}]},"item_4_text_4":{"attribute_name":"著者所属","attribute_value_mlt":[{"subitem_text_value":"Department of Mathematics, Faculty of Science, The M. S. University of Baroda"}]},"item_creator":{"attribute_name":"著者","attribute_type":"creator","attribute_value_mlt":[{"creatorNames":[{"creatorName":"Ghodadra, Bhikha Lila"}],"nameIdentifiers":[{"nameIdentifier":"146120","nameIdentifierScheme":"WEKO"}]}]},"item_files":{"attribute_name":"ファイル情報","attribute_type":"file","attribute_value_mlt":[{"accessrole":"open_date","date":[{"dateType":"Available","dateValue":"2018-04-04"}],"displaytype":"detail","filename":"jms230401.pdf","filesize":[{"value":"146.0 kB"}],"format":"application/pdf","licensetype":"license_note","mimetype":"application/pdf","url":{"label":"jms230401.pdf","url":"https://repository.dl.itc.u-tokyo.ac.jp/record/49244/files/jms230401.pdf"},"version_id":"470725c9-73aa-429d-b6d5-a5ac63c5af8a"}]},"item_keyword":{"attribute_name":"キーワード","attribute_value_mlt":[{"subitem_subject":"Multiple Walsh-Fourier coefficient ","subitem_subject_scheme":"Other"},{"subitem_subject":" Function of bounded p-variation in several variables ","subitem_subject_scheme":"Other"},{"subitem_subject":" order of magnitude ","subitem_subject_scheme":"Other"},{"subitem_subject":" Lacunary Fourier series with small gaps","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":"departmental bulletin paper","resourceuri":"http://purl.org/coar/resource_type/c_6501"}]},"item_title":"On the Coefficients of Multiple Walsh-Fourier Series with Small Gaps","item_titles":{"attribute_name":"タイトル","attribute_value_mlt":[{"subitem_title":"On the Coefficients of Multiple Walsh-Fourier Series with Small Gaps"}]},"item_type_id":"4","owner":"1","path":["7722","7725"],"pubdate":{"attribute_name":"公開日","attribute_value":"2018-04-04"},"publish_date":"2018-04-04","publish_status":"0","recid":"49244","relation_version_is_last":true,"title":["On the Coefficients of Multiple Walsh-Fourier Series with Small Gaps"],"weko_creator_id":"1","weko_shared_id":null},"updated":"2022-12-19T04:24:03.139347+00:00"}