{"paper":{"title":"Hardy-Littlewood maximal operator on the associate space of a Banach function space","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Alexei Yu. Karlovich","submitted_at":"2018-08-16T19:08:36Z","abstract_excerpt":"Let $\\mathcal{E}(X,d,\\mu)$ be a Banach function space over a space of homogeneous type $(X,d,\\mu)$. We show that if the Hardy-Littlewood maximal operator $M$ is bounded on the space $\\mathcal{E}(X,d,\\mu)$, then its boundedness on the associate space $\\mathcal{E}'(X,d,\\mu)$ is equivalent to a certain condition $\\mathcal{A}_\\infty$. This result extends a theorem by Andrei Lerner from the Euclidean setting of $\\mathbb{R}^n$ to the setting of spaces of homogeneous type."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.05645","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"}