{"paper":{"title":"Improvements on Sawyer type estimates for generalized maximal functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Fabio Berra, Gladis Pradolini, Marilina Carena","submitted_at":"2019-03-29T15:34:57Z","abstract_excerpt":"In this paper we prove mixed inequalities for the maximal operator $M_\\Phi$, for general Young functions $\\Phi$ with certain additional properties, improving and generalizing some previous estimates for the Hardy-Littlewood maximal operator proved by E. Sawyer. We show that given $r\\geq 1$, if $u,v^r$ are weights belonging to the $A_1$-Muckenhoupt class and $\\Phi$ is a Young function as above, then the inequality\n  \\[uv^r\\left(\\left\\{x\\in \\mathbb{R}^n: \\frac{M_\\Phi(fv)(x)}{v(x)}>t\\right\\}\\right)\\leq C\\int_{\\mathbb{R}^n}\\Phi\\left(\\frac{|f(x)|}{t}\\right)u(x)v^r(x)\\,dx\\]\n  holds for every positiv"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.00835","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"}