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

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

doi:10.1017/S0013091519000439

Maximal functions associated with families of homogeneous curves: L^p bounds for P ≤ 2

Shaoming Guo, Joris Roos, Andreas Seeger, Po Lam Yung^*

^*Corresponding author for this work

Mathematical Sciences Institute

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

Let M^(u), H^(u) be the maximal operator and Hilbert transform along the parabola (t, ut²). 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.

Original language	English
Pages (from-to)	398-412
Number of pages	15
Journal	Proceedings of the Edinburgh Mathematical Society
Volume	63
Issue number	2
Early online date	3 Feb 2020
DOIs	https://doi.org/10.1017/S0013091519000439
Publication status	E-pub ahead of print - 3 Feb 2020

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title = "Maximal functions associated with families of homogeneous curves: Lp bounds for P ≤ 2",

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.",

keywords = "Hilbert transforms along curves, maximal and singular Radon transforms, maximal functions",

author = "Shaoming Guo and Joris Roos and Andreas Seeger and Yung, {Po Lam}",

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T2 - Lp bounds for P ≤ 2

AU - Guo, Shaoming

AU - Roos, Joris

AU - Seeger, Andreas

AU - Yung, Po Lam

PY - 2020/2/3

Y1 - 2020/2/3

N2 - 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.

AB - 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.

KW - Hilbert transforms along curves

KW - maximal and singular Radon transforms

KW - maximal functions

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DO - 10.1017/S0013091519000439

M3 - Article

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SP - 398

EP - 412

JO - Proceedings of the Edinburgh Mathematical Society

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IS - 2

ER -

Maximal functions associated with families of homogeneous curves: L^p bounds for P ≤ 2

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