{"paper":{"title":"Solyanik estimates in harmonic analysis","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":"2013-10-14T18:31:39Z","abstract_excerpt":"Let $\\mathcal{B}$ denote a collection of open bounded sets in $\\mathbb{R}^n$, and define the associated maximal operator $M_{\\mathcal{B}}$ by $$ M_{\\mathcal{B}}f(x) := \\sup_{x \\in R \\in \\mathcal{B}} \\frac{1}{|R|}\\int_R |f|. $$ The sharp Tauberian constant of $M_{\\mathcal{B}}$ associated to $\\alpha$, denoted by $C_{\\mathcal{B}}(\\alpha)$, is defined as $$ C_{\\mathcal{B}}(\\alpha) := \\sup_{E :\\, 0 < |E| < \\infty}\\frac{1}{|E|}\\big|\\big\\{x \\in \\mathbb{R}^n:\\, M_{\\mathcal{B}}\\chi_E (x) > \\alpha\\big\\}\\big|.$$ Motivated by previous work of A. A. Solyanik, we show that if $M_{\\mathcal{B}}$ is the uncent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.3771","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"}