{"paper":{"title":"Centered Hardy--Littlewood maximal operator on the real line: lower bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Paata Ivanisvili, Samuel Zbarsky","submitted_at":"2018-07-12T02:11:27Z","abstract_excerpt":"For $1<p<\\infty$ and $M$ the centered Hardy-Littlewood maximal operator on $\\mathbb{R}$, we consider whether there is some $\\varepsilon=\\varepsilon(p)>0$ such that $\\|Mf\\|_p\\ge (1+\\varepsilon)||f||_p$. We prove this for $1<p<2$. For $2\\le p<\\infty$, we prove the inequality for indicator functions and for unimodal functions."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.04399","kind":"arxiv","version":2},"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"}