{"id":569,"date":"2026-10-09T11:00:47","date_gmt":"2026-10-09T09:00:47","guid":{"rendered":"https:\/\/mat.uab.cat\/web\/mprats\/?p=569"},"modified":"2026-10-09T11:00:48","modified_gmt":"2026-10-09T09:00:48","slug":"marti-prats-weak-reverse-holder-inequalities-for-doubling-measures","status":"publish","type":"post","link":"https:\/\/mat.uab.cat\/web\/mprats\/2026\/10\/09\/marti-prats-weak-reverse-holder-inequalities-for-doubling-measures\/","title":{"rendered":"Mart\u00ed Prats: Weak reverse H\u00f6lder inequalities for doubling measures"},"content":{"rendered":"\n
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arXiv<\/a><\/div>\n<\/div>\n\n\n\n

Let \u03bc<\/mi><\/mrow><\/semantics><\/math> be a doubling Radon measure in R<\/mi><\/mrow>d<\/mi><\/msup><\/mrow><\/semantics><\/math> with support X<\/mi><\/mrow><\/semantics><\/math>. We prove a local and quantitative form of the Bennewitz–Lewis theorem in this setting: if a Radon measure \u03bd<\/mi><\/mrow><\/semantics><\/math> satisfies the Bennewitz–Lewis condition on a bounded relatively open set V<\/mi>\u2282<\/mo>X<\/mi><\/mrow><\/semantics><\/math> with a small enough constant, then \u03bd<\/mi>|<\/mo><\/mrow>V<\/mi><\/msub>\u226a<\/mo>\u03bc<\/mi>|<\/mo><\/mrow>V<\/mi><\/msub><\/mrow><\/semantics><\/math> and its density satisfies a reverse H\u00f6lder inequality on every compact subset K<\/mi>\u2282<\/mo>V<\/mi><\/mrow><\/semantics><\/math>. Along the way we develop the dyadic toolkit these arguments run on — triple cubes defined through neighbours, the basis D<\/mi><\/mrow>\u222a<\/mo>3<\/mn>D<\/mi><\/mrow><\/mrow><\/semantics><\/math>, and a Whitney decomposition — and we collect the Muckenhoupt-type classes of weights over that basis. The same machinery yields a local Gehring lemma for enlarged balls: both theorems are deduced from a single bootstrapping lemma, stated once for p<\/mi>=<\/mo>1<\/mn><\/mrow><\/semantics><\/math> and p<\/mi>><\/mo>1<\/mn><\/mrow><\/semantics><\/math>.<\/p>\n","protected":false},"excerpt":{"rendered":"

Let \u03bc be a doubling Radon measure in Rd with support X. We prove a local and quantitative form of the Bennewitz–Lewis theorem in this setting: if a Radon measure \u03bd satisfies the Bennewitz–Lewis condition on a bounded relatively open set V\u2282X with a small enough constant, then \u03bd|V\u226a\u03bc|V and its density satisfies a reverse … Continua la lectura de Mart\u00ed Prats: Weak reverse H\u00f6lder inequalities for doubling measures<\/span> →<\/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-569","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\/569","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=569"}],"version-history":[{"count":1,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/569\/revisions"}],"predecessor-version":[{"id":570,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/posts\/569\/revisions\/570"}],"wp:attachment":[{"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/media?parent=569"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/categories?post=569"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mat.uab.cat\/web\/mprats\/wp-json\/wp\/v2\/tags?post=569"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}