{"paper":{"title":"Critical exponents of the Riesz projection","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Adri\\'an Llinares, Kristian Seip, Ole Fredrik Brevig","submitted_at":"2024-02-15T08:35:35Z","abstract_excerpt":"Let $\\mathfrak{p}_d(q)$ denote the critical exponent of the Riesz projection from $L^q(\\mathbb{T}^d)$ to the Hardy space $H^p(\\mathbb{T}^d)$, where $\\mathbb{T}$ is the unit circle. We present the state-of-the-art on the conjecture that $\\mathfrak{p}_1(q) = 4(1-1/q)$ for $1 \\leq q \\leq \\infty$ and prove that it holds in the endpoint case $q = 1$. We then extend the conjecture to \\[\\mathfrak{p}_d(q) = 2+\\cfrac{2}{d+\\cfrac{2}{q-2}}\\] for $d\\geq1$ and $\\frac{2d}{d+1} \\leq q \\leq \\infty$ and establish that if the conjecture holds for $d=1$, then it also holds for $d=2$. When $d=2$, we verify that t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2402.09787","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/2402.09787/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"}