{"id":94,"date":"2019-10-05T14:24:20","date_gmt":"2019-10-05T12:24:20","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/mprats\/?p=94"},"modified":"2025-07-09T15:25:04","modified_gmt":"2025-07-09T13:25:04","slug":"marti-prats-measuring-triebel-lizorkin-fractional-smoothness-on-domains-in-terms-of-first-order-differences","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/mprats\/2019\/10\/05\/marti-prats-measuring-triebel-lizorkin-fractional-smoothness-on-domains-in-terms-of-first-order-differences\/","title":{"rendered":"Mart\u00ed Prats: Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences"},"content":{"rendered":"\n<div class=\"wp-block-group is-nowrap is-layout-flex wp-container-core-group-is-layout-ad2f72ca wp-block-group-is-layout-flex\">\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/arxiv.org\/abs\/1804.05780\" target=\"_blank\" rel=\"noreferrer noopener\">arXiv<\/a><\/div>\n<\/div>\n\n\n\n<div class=\"wp-block-buttons is-layout-flex wp-block-buttons-is-layout-flex\">\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"https:\/\/doi.org\/10.1112\/jlms.12225\" target=\"_blank\" rel=\"noreferrer noopener\">JLMS<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n\n\n\n\n<p>In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space \\(F_{p,q}^s(\\Omega)\\) in terms of first-order differences in a uniform domain \\(\\Omega\\). The characterization is valid for any positive, non-integer real smoothness \\(s\\in \\mathbb{R}_+\\setminus \\mathbb{N}\\) and indices \\( 1 \\leq p &lt; \\infty \\), \\(1\\leq q \\leq \\infty\\) as long as the fractional part \\(s\\) is greater than \\(d\/p-d\/q\\).<\/p>\n\n\n\n<p><\/p>\n","protected":false},"excerpt":{"rendered":"<p>In this note we give equivalent characterizations for a fractional Triebel-Lizorkin space \\(F_{p,q}^s(\\Omega)\\) in terms of first-order differences in a uniform domain \\(\\Omega\\). The characterization is valid for any positive, non-integer real smoothness \\(s\\in \\mathbb{R}_+\\setminus \\mathbb{N}\\) and indices \\( 1 \\leq p &lt; \\infty \\), \\(1\\leq q \\leq \\infty\\) as long as the fractional part &hellip; <a href=\"https:\/\/mat.uab.cat\/web\/mprats\/2019\/10\/05\/marti-prats-measuring-triebel-lizorkin-fractional-smoothness-on-domains-in-terms-of-first-order-differences\/\" class=\"more-link\">Continua la lectura de <span class=\"screen-reader-text\">Mart\u00ed Prats: Measuring Triebel-Lizorkin fractional smoothness on domains in terms of first-order differences<\/span> <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":53,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[95],"tags":[39],"class_list":["post-94","post","type-post","status-publish","format-standard","hentry","category-papers-en","tag-papers-en"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/94","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/users\/53"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/comments?post=94"}],"version-history":[{"count":4,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/94\/revisions"}],"predecessor-version":[{"id":452,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/94\/revisions\/452"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/media?parent=94"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/categories?post=94"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/tags?post=94"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}