{"paper":{"title":"The weak type $(1,1)$ bounds for the maximal function associated to cubes grow to infinity with the dimension","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"J. M. Aldaz","submitted_at":"2008-05-11T22:21:13Z","abstract_excerpt":"Let $M_d$ be the centered Hardy-Littlewood maximal function associated to cubes in $\\mathbb{R}^d$ with Lebesgue measure, and let $c_d$ denote the lowest constant appearing in the weak type (1,1) inequality satisfied by $M_d$.\n  We show that $c_d \\to \\infty$ as $d\\to \\infty$, thus answering, for the case of cubes, a long standing open question of E. M. Stein and J. O. Str\\\"{o}mberg."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0805.1565","kind":"arxiv","version":5},"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"}