Maximal functions associated with families of homogeneous curves: Lp bounds for P ≤ 2

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

Type: Article

Publication Date: 2020-02-03

Citations: 4

DOI: https://doi.org/10.1017/s0013091519000439

Abstract

Abstract Let M ( u ) , H ( u ) be the maximal operator and Hilbert transform along the parabola ( t , ut 2 ). For U ⊂ (0, ∞) we consider L p 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.

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Maximal functions associated with families of homogeneous curves: <i>L</i><sup><i>p</i></sup> bounds for <i>P</i> ≤ 2

Abstract

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