{"id":93536,"date":"2018-03-11T10:12:58","date_gmt":"2018-03-11T10:12:58","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/the-c1-harmonic-capacity-and-the-riesz-transform\/"},"modified":"2018-03-11T10:12:58","modified_gmt":"2018-03-11T10:12:58","slug":"the-c1-harmonic-capacity-and-the-riesz-transform","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/teoria-de-la-aproximacion\/the-c1-harmonic-capacity-and-the-riesz-transform\/","title":{"rendered":"The c1 harmonic capacity and the riesz transform"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Aleix Ruiz De Villa Robert <\/strong><\/h2>\n<p>La tesis consta de tres resultados principales. El primero es la demostraci\u00f3n de la semiaditividad de la capacidad c^1 arm\u00f3nica. \u00e9sta puede entenderse como una generalizaci\u00f3n en r^n de la capacidad anal\u00edtica definida en el plano complejo. El estudio de la capacidad c^1 arm\u00f3nica tiene aplicaciones directas en el campo de la aproximaci\u00f3n uniforme de funciones continuas por funciones arm\u00f3nicas. El segundo resultado consiste en acotar la integral de la derivada normal de una funci\u00f3n f sobre la frontera de un dominio lipschitz en t\u00e9rminos de la capacidad c^1 arm\u00f3nica del soporte del laplaciano de f. Este resultado generaliza un resultado an\u00e1logo en t\u00e9rminos de la capacidad anal\u00edtica. En ambos casos, no s\u00f3lo ha sido necesario adaptar aquellas herramientas utilizadas en resultados previos, sin\u00f3 que adem\u00e1s se han tenido que combinar con t\u00e9cnicas m\u00e1s complicadas. El tercer resultado ha sido demostrar que el valor pincipal de las transformadas de riesz s-dimensionales de una medida con densidad superior positiva y finita, no puede existir si s no es un valor entero. El mismo resultado hab\u00eda sido obtenido con medidas con densidad inferior positiva y finita. Nuevas t\u00e9cnicas han sido utilizadas para demostrar este \u00faltimo resultado de la tesis.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>The c1 harmonic capacity and the riesz transform<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 The c1 harmonic capacity and the riesz transform <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Aleix Ruiz De Villa Robert <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 27\/05\/2009<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<h3>Direcci\u00f3n y tribunal<\/h3>\n<ul>\n<li><strong>Director de la tesis<\/strong>\n<ul>\n<li>Javier Tolsa Domenech<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: pertti Mattila <\/li>\n<li>carme Cascante canut (vocal)<\/li>\n<li>  (vocal)<\/li>\n<li>  (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Aleix Ruiz De Villa Robert La tesis consta de tres resultados principales. El primero es la demostraci\u00f3n [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"footnotes":""},"categories":[12647,41797],"tags":[193138,193140,193139,96500],"class_list":["post-93536","post","type-post","status-publish","format-standard","hentry","category-teoria-de-la-aproximacion","category-transformadas-integrales","tag-aleix-ruiz-de-villa-robert","tag-carme-cascante-canut","tag-javier-tolsa-domenech","tag-pertti-mattila"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/93536","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/comments?post=93536"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/93536\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=93536"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=93536"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=93536"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}