{"id":58,"date":"2017-10-05T13:10:04","date_gmt":"2017-10-05T11:10:04","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/mprats\/?p=58"},"modified":"2025-07-09T15:37:06","modified_gmt":"2025-07-09T13:37:06","slug":"marti-prats-and-eero-saksman-a-t1-theorem-for-fractional-sobolev-spaces-on-domains","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/mprats\/2017\/10\/05\/marti-prats-and-eero-saksman-a-t1-theorem-for-fractional-sobolev-spaces-on-domains\/","title":{"rendered":"Mart\u00ed Prats and Eero Saksman: A T(1) theorem for fractional Sobolev spaces on domains"},"content":{"rendered":"\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\/1507.03935\" target=\"_blank\" rel=\"noreferrer noopener\">arXiv (2019 version)<\/a><\/div>\n\n\n\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"http:\/\/dx.doi.org\/10.1007\/s12220-017-9770-y\" target=\"_blank\" rel=\"noreferrer noopener\">J. Geom. Anal.<\/a><\/div>\n<\/div>\n\n\n\n\n\n\n\n<p>Given any uniform domain \\( \\Omega \\), the Triebel-Lizorkin space \\( F^s_{p,q}(\\Omega) \\) with \\( 0 &lt; s &lt; 1 \\) and \\( 1 &lt; p,q &lt; \\infty \\) can be equipped with a norm in terms of first order differences restricted to pairs of points whose distance is comparable to their distance to the boundary. Using this characterization, originally due to Seeger and reproven here, we prove a T(1)-theorem for fractional Sobolev spaces with \\( 0 &lt; s &lt; 1 \\) for any uniform domain and for a large family of Calder\u00f3n-Zygmund operators in any ambient space \\( \\mathbb{R}^d \\) as long as \\( sp&gt;d \\).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Given any uniform domain \\( \\Omega \\), the Triebel-Lizorkin space \\( F^s_{p,q}(\\Omega) \\) with \\( 0 &lt; s &lt; 1 \\) and \\( 1 &lt; p,q &lt; \\infty \\) can be equipped with a norm in terms of first order differences restricted to pairs of points whose distance is comparable to their distance to the &hellip; <a href=\"https:\/\/mat.uab.cat\/web\/mprats\/2017\/10\/05\/marti-prats-and-eero-saksman-a-t1-theorem-for-fractional-sobolev-spaces-on-domains\/\" class=\"more-link\">Continua la lectura de <span class=\"screen-reader-text\">Mart\u00ed Prats and Eero Saksman: A T(1) theorem for fractional Sobolev spaces on domains<\/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-58","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\/58","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=58"}],"version-history":[{"count":5,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/58\/revisions"}],"predecessor-version":[{"id":459,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/58\/revisions\/459"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/media?parent=58"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/categories?post=58"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/tags?post=58"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}