Maximal functions associated with families of homogeneous curves

Guo, Shaoming; Roos, Joris; Seeger, Andreas; Yung, Po Lam

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Maximal functions associated with families of homogeneous curves

Date

2020-05-01

Authors

Abstract

Let 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.