{"paper":{"title":"Sharp inequalities for one-sided Muckenhoupt weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ioannis Parissis, Olli Saari, Paul A. Hagelstein","submitted_at":"2016-01-05T18:58:15Z","abstract_excerpt":"Let $A_\\infty ^+$ denote the class of one-sided Muckenhoupt weights, namely all the weights $w$ for which $\\mathsf M^+:L^p(w)\\to L^{p,\\infty}(w)$ for some $p>1$, where $\\mathsf M^+$ is the forward Hardy-Littlewood maximal operator. We show that $w\\in A_\\infty ^+$ if and only if there exist numerical constants $\\gamma\\in(0,1)$ and $c>0$ such that $$ w(\\{x \\in \\mathbb{R} : \\, \\mathsf M ^+\\mathbf 1_E (x)>\\gamma\\})\\leq c w(E) $$ for all measurable sets $E\\subset \\mathbb R$. Furthermore, letting $$ \\mathsf C_w ^+(\\alpha):= \\sup_{0<w(E)<+\\infty} \\frac{1}{w(E)} w(\\{x\\in\\mathbb R:\\,\\mathsf M^+\\mathbf "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.00938","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}