{"paper":{"title":"Weak-type (1,1) estimates for strongly singular operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Magali Folch-Gabayet, Ricardo A. S\\'aenz","submitted_at":"2018-02-13T17:59:50Z","abstract_excerpt":"Let $\\psi$ be a positive function defined near the origin such that $\\lim_{t\\to 0^{+}}\\psi(t)=0$. We consider the operator \\begin{equation*} T_\\theta f(x) = \\lim_{\\varepsilon\\to 0^+} \\int_\\varepsilon^1 e^{i\\gamma(t)}f(x-t) \\frac{dt}{t^{\\theta}\\psi(t)^{1-\\theta}}, \\end{equation*} where $\\gamma$ is a real function with $\\lim_{t\\to 0^+}|\\gamma(t)| = \\infty$ and $0 \\le \\theta \\le 1$. Assuming certain regularity and growth conditions on $\\psi$ and $\\gamma$, we show that $T_1$ is of weak type $(1,1)$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.04767","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"}