{"id":82,"date":"2017-10-05T14:17:32","date_gmt":"2017-10-05T12:17:32","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/mprats\/?p=82"},"modified":"2025-07-09T15:29:08","modified_gmt":"2025-07-09T13:29:08","slug":"marcos-oliva-and-marti-prats-sharp-bounds-for-composition-with-quasiconformal-mappings-in-sobolev-spaces","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/mprats\/2017\/10\/05\/marcos-oliva-and-marti-prats-sharp-bounds-for-composition-with-quasiconformal-mappings-in-sobolev-spaces\/","title":{"rendered":"Marcos Oliva and Mart\u00ed Prats: Sharp bounds for composition with quasiconformal mappings in Sobolev spaces"},"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\/1612.00689\" 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<div class=\"wp-block-button\"><a class=\"wp-block-button__link wp-element-button\" href=\"http:\/\/dx.doi.org\/10.1016\/j.jmaa.2017.02.016\" target=\"_blank\" rel=\"noreferrer noopener\">JMAA<\/a><\/div>\n<\/div>\n<\/div>\n\n\n\n\n\n\n\n<p>Let \\( \\phi \\) be a quasiconformal mapping, and let \\( T_\\phi \\) be the composition operator which maps \\( f \\) to \\( f\\circ\\phi \\). Since \\( \\phi \\) may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins with the behavior of \\( T_\\phi\\) on \\(L^p \\) and \\(W^{1,p} \\) for \\(1 &lt; p &lt; \\infty \\). This cases are well understood but alternative proofs of some known results are provided. Using interpolation techniques it is seen that compactly supported Bessel potential functions in \\(H^{s,p} \\) are sent to \\(H^{s,q} \\) whenever \\(0 &lt; s &lt; 1 \\) for appropriate values of \\(q \\). The techniques used lead to sharp results and they can be applied to Besov spaces as well.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let \\( \\phi \\) be a quasiconformal mapping, and let \\( T_\\phi \\) be the composition operator which maps \\( f \\) to \\( f\\circ\\phi \\). Since \\( \\phi \\) may not be bi-Lipschitz, the composition operator need not map Sobolev spaces to themselves. The study begins with the behavior of \\( T_\\phi\\) on \\(L^p &hellip; <a href=\"https:\/\/mat.uab.cat\/web\/mprats\/2017\/10\/05\/marcos-oliva-and-marti-prats-sharp-bounds-for-composition-with-quasiconformal-mappings-in-sobolev-spaces\/\" class=\"more-link\">Continua la lectura de <span class=\"screen-reader-text\">Marcos Oliva and Mart\u00ed Prats: Sharp bounds for composition with quasiconformal mappings in Sobolev spaces<\/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-82","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\/82","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=82"}],"version-history":[{"count":6,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/82\/revisions"}],"predecessor-version":[{"id":458,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/82\/revisions\/458"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/media?parent=82"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/categories?post=82"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/tags?post=82"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}