{"id":204,"date":"2025-07-02T11:14:29","date_gmt":"2025-07-02T10:14:29","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/tfg\/?p=204"},"modified":"2025-07-02T11:14:29","modified_gmt":"2025-07-02T10:14:29","slug":"interpolacio-doperadors","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/tfg\/interpolacio-doperadors\/","title":{"rendered":"Interpolaci\u00f3 d&#8217;Operadors"},"content":{"rendered":"<p data-start=\"162\" data-end=\"597\">La teoria de la interpolaci\u00f3 d\u2019operadors es va iniciar amb una observaci\u00f3 de J\u00f3\u017cef Marcinkiewicz, posteriorment generalitzada i ara coneguda com el teorema de Riesz-Thorin. En termes simples, si un operador lineal \u00e9s acotat en un espai \\(L^p\\) i tamb\u00e9 en un espai \\(L^q\\), llavors \u00e9s cont\u00ednuament extensible a qualsevol espai \\(L^r\\) amb \\(r\\) entre \\(p\\) i \\(q\\). En altres paraules, l&#8217;espai \\(L^r\\) actua com a espai intermedi entre \\(L^p\\) i \\(L^q\\).<\/p>\n<p data-start=\"599\" data-end=\"1077\">L\u2019objectiu \u00e9s demostrar els teoremes cl\u00e0ssics en el camp de la\u00a0 interpolaci\u00f3 d\u2019operadors: el <strong data-start=\"694\" data-end=\"736\">Teorema d\u2019Interpolaci\u00f3 de Riesz-Thorin<\/strong>, aplicable a operadors de tipus fort, i el <strong data-start=\"780\" data-end=\"823\">Teorema\u00a0 d\u2019Interpolaci\u00f3 de Marcinkiewicz<\/strong>, adequat per a operadors de tipus feble. A m\u00e9s, es presentaran aplicacions rellevants d\u2019aquests teoremes, com ara l\u2019acotaci\u00f3 de l\u2019<strong data-start=\"954\" data-end=\"994\">operador maximal de Hardy-Littlewood<\/strong>, la <strong data-start=\"999\" data-end=\"1026\">transformada de Fourier<\/strong> i la <strong data-start=\"1032\" data-end=\"1056\">desigualtat de Young<\/strong> per a la convoluci\u00f3.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>La teoria de la interpolaci\u00f3 d\u2019operadors es va iniciar amb una observaci\u00f3 de J\u00f3\u017cef Marcinkiewicz, posteriorment generalitzada i ara coneguda com el teorema de Riesz-Thorin. En termes simples, si un operador lineal \u00e9s acotat en un espai \\(L^p\\) i tamb\u00e9 en un espai \\(L^q\\), llavors \u00e9s cont\u00ednuament extensible a qualsevol espai \\(L^r\\) amb \\(r\\) entre [&hellip;]<\/p>\n","protected":false},"author":71,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[29],"tags":[37],"class_list":["post-204","post","type-post","status-publish","format-standard","hentry","category-analisi-matematica","tag-joaquim-martin"],"_links":{"self":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/204","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/users\/71"}],"replies":[{"embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/comments?post=204"}],"version-history":[{"count":2,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/204\/revisions"}],"predecessor-version":[{"id":207,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/posts\/204\/revisions\/207"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/media?parent=204"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/categories?post=204"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/tfg\/wp-json\/wp\/v2\/tags?post=204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}