{"paper":{"title":"On the $l^p$-norm of the discrete Hilbert transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.FA","math.PR"],"primary_cat":"math.CA","authors_text":"Mateusz Kwa\\'snicki, Rodrigo Ba\\~nuelos","submitted_at":"2017-09-21T17:41:40Z","abstract_excerpt":"Using a representation of the discrete Hilbert transform in terms of martingales arising from Doob $h$-processes, we prove that its $l^p$-norm, $1<p<\\infty$, is bounded above by the $L^p$-norm of the continuous Hilbert transform. Together with the already known lower bound, this resolves the long-standing conjecture that the norms of these operators are equal."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.07427","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"}