{"paper":{"title":"A note on local H\\\"older continuity of weighted Tauberian functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ioannis Parissis, Paul A. Hagelstein","submitted_at":"2015-03-10T13:33:53Z","abstract_excerpt":"Let $\\mathsf M$ and $\\mathsf M _{\\mathsf S}$ respectively denote the Hardy-Littlewood maximal operator with respect to cubes and the strong maximal operator on $\\mathbb{R}^n$, and let $w$ be a nonnegative locally integrable function on $\\mathbb{R}^n$. We define the associated Tauberian functions $\\mathsf{C}_{\\mathsf{HL},w}(\\alpha)$ and $\\mathsf{C}_{\\mathsf{S},w}(\\alpha)$ on $(0,1)$ by \\[\n  \\mathsf{C}_{\\mathsf{HL},w}(\\alpha) :=\\sup_{\\substack{E \\subset \\mathbb{R}^n \\\\ 0 < w(E) < \\infty}} \\frac{1}{w(E)}w(\\{x \\in \\mathbb{R}^n : \\mathsf M \\chi_E(x) > \\alpha\\}) \\] and \\[ \\mathsf{C}_{\\mathsf{S},w}(\\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02898","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"}