{"paper":{"title":"Variable Muckenhoupt $A_\\infty$ Weights","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.FA","authors_text":"Dachun Yang, Wen Yuan, Zongze Zeng","submitted_at":"2026-05-13T03:22:31Z","abstract_excerpt":"In this article, with introducing concepts of variable scalar $\\mathcal{A}_{p(\\cdot),\\infty}$ weights and variable matrix $\\mathscr{A}_{p(\\cdot),\\infty}$ weights, we seek a comprehensive theory of $A_\\infty$ weights within the framework of variable exponent spaces. We first show that a weight belongs to $\\mathcal{A}_{p(\\cdot),\\infty}$ if and only if its $p(\\cdot)$-th power is an $A_\\infty$ weight. Using this, we characterize the $\\mathcal{A}_{p(\\cdot),\\infty}$ condition by the minimal operator. Then we establish the reverse H\\\"older's inequality for $\\mathcal{A}_{p(\\cdot),\\infty}$ weights in v"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.12941","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"}