{"paper":{"title":"Maximal functions associated to flat plane curves with Mitigating factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ramesh Manna","submitted_at":"2016-09-26T19:53:46Z","abstract_excerpt":"We study the boundedness problem for maximal operators $\\mathbb{M}_{\\sigma}$ associated to flat plane curves with Mitigating factors, defined by $$\\mathbb{M}_{\\sigma}f(x) \\, := \\, \\sup_{1 \\leq t \\leq 2} \\left|\\int_{0}^{1} f(x-t\\Gamma(s)) \\, (\\kappa(s))^{\\sigma} \\, ds\\right|,$$ where $\\kappa(s)$ denotes the curvature of the curve $\\Gamma(s)=(s, g(s)+1), ~g(s) \\in C^5[0,1]$ in $\\mathbb{R}^2$. Let $\\triangle$ be the closed triangle with vertices $P=(\\frac{2}{5}, \\frac{1}{5}), ~ Q=(\\frac{1}{2}, \\frac{1}{2}), ~ R=(0, 0).$\n  In this paper, we prove that for $ (\\frac{1}{p}, \\frac{1}{q}) \\in \\left[(\\f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.08140","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"}