{"paper":{"title":"Inversion and extension of the finite Hilbert transform on (-1,1)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Guillermo P. Curbera, Susumu Okada, Werner J. Ricker","submitted_at":"2019-01-18T16:47:03Z","abstract_excerpt":"The principle of optimizing inequalities, or their equivalent operator theoretic formulation, is well established in analysis. For an operator, this corresponds to extending its action to larger domains, hopefully to the largest possible such domain (i.e, its \\textit{optimal domain}). Some classical operators are already optimally defined (e.g., the Hilbert transform in $L^p(\\mathbb{R})$, $1<p<\\infty$) and others are not (e.g., the Hausdorff-Young inequality in $L^p(\\mathbb{T})$, $1<p<2$, or Sobolev's inequality in various spaces). In this paper a detailed investigation is undertaken of the fi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.06334","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"}