{"paper":{"title":"Mixed weak estimates of Sawyer type for generalized maximal operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Fabio Berra","submitted_at":"2018-08-13T17:17:28Z","abstract_excerpt":"We study mixed weak estimates of Sawyer type for maximal operators associated to the family of Young functions $\\Phi(t)=t^r(1+\\log^+t)^{\\delta}$, where $r\\geq 1$ and $\\delta\\geq 0$. More precisely, if $u$ and $v^r$ are $A_1$ weights, and $w$ is defined as $w=1/\\Phi(v^{-1})$ then the following estimate \\[uw\\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)|v(x)}{t}\\right)u(x) \\,dx\\] holds for every positive $t$. This extends mixed estimates to a wider class of maximal operators, since when we put $r=1$ and $\\delta=0$ we "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.04333","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"}