{"id":36453,"date":"1998-01-01T00:00:00","date_gmt":"1998-01-01T00:00:00","guid":{"rendered":"https:\/\/www.deberes.net\/tesis\/sin-categoria\/curvatura-de-medidas-integral-singular-de-cauchy-y-capacidad-analitica\/"},"modified":"1998-01-01T00:00:00","modified_gmt":"1998-01-01T00:00:00","slug":"curvatura-de-medidas-integral-singular-de-cauchy-y-capacidad-analitica","status":"publish","type":"post","link":"https:\/\/www.deberes.net\/tesis\/matematicas\/curvatura-de-medidas-integral-singular-de-cauchy-y-capacidad-analitica\/","title":{"rendered":"Curvatura de medidas, integral singular de cauchy y capacidad analitica"},"content":{"rendered":"<h2>Tesis doctoral de <strong> Xavier Tolsa Domenech <\/strong><\/h2>\n<p>En esta tesis se caracterizan todas las medidas no at\u00f3micas    (no necesariamente doblantes) para las cuales el operador integral de cauchy es acotado en l2(  ). Esta caracterizaci\u00f3n se realiza en t\u00e9rminos de la curvatura de la medida    . El resultado obtenido es equivalente a un teorema de tipo t (1) para el operador integral de cauchy v\u00e1lido para medidas no doblantes. Tambi\u00e9n se estudia la acotaci\u00f3n en lp (   ) y la acotaci\u00f3n de tipo d\u00e9bil (1,1).  a partir de estos resultados se pueden obtener estimaciones sobre la capacidad anal\u00edtica gamma. Adem\u00e1s permiten caracterizar geom\u00e9tricamente la capacidad gamma+ de un conjunto compacto.  asimismo se obtienen diversos resultados sobre la existencia de valores principales para la integral de cauchy. Se demuestra que la acotaci\u00f3n en l2 (   ) implica la existencia de valores principales. Dada una medida   , se prueba que existen los valores principales de la integral de cauchy de cualquier medida compleja    en casi todo punto respecto de    si y solo si la densidad superior (lineal) de es finita en casi todo punto respecto de    y la curvatura de   es   -finita.<\/p>\n<p>&nbsp;<\/p>\n<h3>Datos acad\u00e9micos de la tesis doctoral \u00ab<strong>Curvatura de medidas, integral singular de cauchy y capacidad analitica<\/strong>\u00ab<\/h3>\n<ul>\n<li><strong>T\u00edtulo de la tesis:<\/strong>\u00a0 Curvatura de medidas, integral singular de cauchy y capacidad analitica <\/li>\n<li><strong>Autor:<\/strong>\u00a0 Xavier Tolsa Domenech <\/li>\n<li><strong>Universidad:<\/strong>\u00a0 Aut\u00f3noma de barcelona<\/li>\n<li><strong>Fecha de lectura de la tesis:<\/strong>\u00a0 01\/01\/1998<\/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>Mark Melnikov<\/li>\n<\/ul>\n<\/li>\n<li><strong>Tribunal<\/strong>\n<ul>\n<li>Presidente del tribunal: Pertti Mattila <\/li>\n<li>M. Jes\u00fas Carro Rossell (vocal)<\/li>\n<li>Joaquim Bruna Floris (vocal)<\/li>\n<li>Jos\u00e9 Luis Fernandez  Perez (vocal)<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Tesis doctoral de Xavier Tolsa Domenech En esta tesis se caracterizan todas las medidas no at\u00f3micas (no necesariamente doblantes) para [&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":[5924,3183,37498,126],"tags":[37501,15064,71591,96499,96500,96498],"class_list":["post-36453","post","type-post","status-publish","format-standard","hentry","category-analisis-armonico","category-analisis-y-analisis-funcional","category-funciones-de-una-variable-compleja","category-matematicas","tag-joaquim-bruna-floris","tag-jose-luis-fernandez-perez","tag-m-jesus-carro-rossell","tag-mark-melnikov","tag-pertti-mattila","tag-xavier-tolsa-domenech"],"_links":{"self":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/36453","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=36453"}],"version-history":[{"count":0,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/posts\/36453\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/media?parent=36453"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/categories?post=36453"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.deberes.net\/tesis\/wp-json\/wp\/v2\/tags?post=36453"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}