{"paper":{"title":"Tauberian conditions, Muckenhoupt weights, and differentiation properties of weighted bases","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.CA","authors_text":"Ioannis Parissis, Paul A. Hagelstein, Teresa Luque","submitted_at":"2013-04-03T17:17:38Z","abstract_excerpt":"We give an alternative characterization of the class of Muckenhoupt weights $A_{\\infty, \\mathfrak B}$ for homothecy invariant Muckenhoupt bases $\\mathfrak B$ consisting of convex sets. In particular we show that $w\\in A_{\\infty, \\mathfrak B}$ if and only if there exists a constant $c>0$ such that for all measurable sets $E\\subset \\mathbb R^n$ we have $$ w({x\\in \\mathbb R^n: M_{\\mathfrak B} (\\mathbf {1}_E)(x)>1/2}) < c w(E).$$ This applies for example to the collection $\\mathfrak R$ of rectangles with sides parallel to the coordinate axes, giving a new characterization of strong (multiparameter"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.1015","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"}