Guo, ShaomingRoos, JorisSeeger, AndreasYung, Po Lam2026-01-012026-01-010013-0915ORCID:/0000-0002-0441-3625/work/164552548https://hdl.handle.net/1885/733800047Let M(u), H(u) be the maximal operator and Hilbert transform along the parabola (t, ut2). For U (0, ∞) we consider Lp estimates for the maximal functions sup u U|M(u)f| and sup u U|H(u)f|, when 1 < p ≤ 2. The parabolas can be replaced by more general non-flat homogeneous curves.Acknowledgements. S.G. was supported in part by NSF grant 1800274. A.S. was supported in part by NSF grant 1764295. P.Y. was partially supported by a General Research Fund CUHK14303817 from the Hong Kong Research Grant Council, and a direct grant for research from the Chinese University of Hong Kong (4053341).15enPublisher Copyright: © 2020 Edinburgh Mathematical Society.Hilbert transforms along curvesmaximal and singular Radon transformsmaximal functions2019-06-1310.1017/S001309151900043985079515440