{"paper":{"title":"Bilinear Calder\\'{o}n-Zygmund operators on Vilenkin groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Adil Shafi Wani, Qaiser Jahan, Salman Ashraf","submitted_at":"2026-06-30T08:55:23Z","abstract_excerpt":"In this article, we study bilinear Calder\\'on--Zygmund operators on a Vilenkin group $G$. As a preliminary step, we establish a Grafakos--Torres-type endpoint weak-type result in our setting. Furthermore, we prove that such operators extend to bounded bilinear mappings from $L^{p_1}(G)\\times L^{p_2}(G)$ into $L^p(G)$ under the natural condition $\\frac{1}{p}=\\frac{1}{p_1}+\\frac{1}{p_2}.$ We then obtain a corresponding boundedness result in Morrey spaces, showing that these operators extend to bounded bilinear mappings from $\\mathcal{M}_{p_1,u_1}(G)\\times \\mathcal{M}_{p_2,u_2}(G)$ into $\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.31360","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.31360/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}