{"paper":{"title":"Endpoint Criteria for One-Dimensional Bilinear Rough Singular Integrals","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Binwei Dan, Qingying Xue","submitted_at":"2026-07-19T11:55:43Z","abstract_excerpt":"We prove endpoint theorems for one-dimensional bilinear rough singular integrals. Our starting point is a sharp structural characterization of the associated angular multiplier. For every mean-zero $\\Omega\\in L^1(\\mathbb{S}^1)$, the finite-part angular multiplier associated with $T_\\Omega$ has bounded variation if and only if the antipodal even part of $\\Omega$ belongs to $H^1(\\mathbb{S}^1)$. This characterization identifies the precise rotational regularity required in the one-dimensional bilinear setting. It also yields a Stieltjes decomposition compatible with uniform estimates for the bili"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2607.17207","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/2607.17207/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"}