{"paper":{"title":"A simple proof that the Riesz projection is bounded on $L^p(\\mathbb{T})$ for $1<p<\\infty$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ole Fredrik Brevig","submitted_at":"2026-05-06T07:26:13Z","abstract_excerpt":"Let $\\mathbf{P}$ denote the Riesz projection on the unit circle $\\mathbb{T}$ and suppose that $1<p<\\infty$. We present a simple proof of the bound $\\|\\mathbf{P}f\\|_p \\leq \\max(p,q) \\|f\\|_p$, where $f$ is in $L^p(\\mathbb{T})$ and $p^{-1}+q^{-1}=1$. Our proof is a variation of a classical argument due to M. Riesz demonstrating that the Hilbert transform is bounded on $L^p(\\mathbb{T})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.05190","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/2606.05190/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"}