{"paper":{"title":"Maximal operators and Hilbert transforms along variable non-flat homogeneous curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jonathan Hickman, Joris Roos, Shaoming Guo, Victor Lie","submitted_at":"2016-10-17T16:51:53Z","abstract_excerpt":"We prove that the maximal operator associated with variable homogeneous planar curves $(t, u t^{\\alpha})_{t\\in \\mathbb{R}}$, $\\alpha\\not=1$ positive, is bounded on $L^p(\\mathbb{R}^2)$ for each $p>1$, under the assumption that $u:\\mathbb{R}^2 \\to \\mathbb{R}$ is a Lipschitz function. Furthermore, we prove that the Hilbert transform associated with $(t, ut^{\\alpha})_{t\\in \\mathbb{R}}$, $\\alpha\\not=1$ positive, is bounded on $L^p(\\mathbb{R}^2)$ for each $p>1$, under the assumption that $u:\\mathbb{R}^2\\to \\mathbb{R}$ is a measurable function and is constant in the second variable. Our proofs rely o"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05203","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"}