{"paper":{"title":"On the Boundedness of The Bilinear Hilbert Transform along \"non-flat\" smooth curves. The Banach triangle case ($L^r,\\: 1\\leq r<\\infty$)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Victor Lie","submitted_at":"2015-12-31T19:58:38Z","abstract_excerpt":"We show that the bilinear Hilbert transform $H_{\\Gamma}$ along curves $\\Gamma=(t,-\\gamma(t))$ with $\\gamma\\in\\mathcal{N}\\mathcal{F}^{C}$ is bounded from $L^{p}(\\mathbb{R})\\times L^{q}(\\mathbb{R})\\,\\rightarrow\\,L^{r}(\\mathbb{R})$ where $p,\\,q,\\,r$ are H\\\"older indices, i.e. $\\frac{1}{p}+\\frac{1}{q}=\\frac{1}{r}$, with $1<p<\\infty$, $1<q\\leq\\infty$ and $1\\leq r<\\infty$. Here $\\mathcal{N}\\mathcal{F}^{C}$ stands for a wide class of smooth \"non-flat\" curves near zero and infinity whose precise definition is given in Section 2. This continues author's earlier work on this topic, extending the bounded"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.09356","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"}