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: Lp bounds for p _ 2

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

School of Mathematics

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

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 supu∈U|M(u)f| and supu∈U|H(u)f|, when 1<p≤2. The parabolae can be replaced by more general non-flat homogeneous curves.

Original language	English
Pages (from-to)	398-412
Number of pages	14
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	Published - 31 May 2020

Access to Document

10.1017/S0013091519000439

1906.05997Accepted author manuscript, 191 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND)

https://arxiv.org/abs/1906.05997

Cite this

@article{c3e6719448c647ad932160c5c940520b,

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 supu∈U|M(u)f| and supu∈U|H(u)f|, when 1<p≤2. The parabolae can be replaced by more general non-flat homogeneous curves. ",

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

year = "2020",

month = may,

day = "31",

doi = "10.1017/S0013091519000439",

language = "English",

volume = "63",

pages = "398--412",

journal = "Proceedings of the Edinburgh Mathematical Society",

issn = "0013-0915",

publisher = "Cambridge University Press",

number = "2",

}

TY - JOUR

T1 - Maximal functions associated with families of homogeneous curves: Lp bounds for p _ 2

AU - Guo, Shaoming

AU - Roos, Joris

AU - Seeger, Andreas

AU - Yung, Po-Lam

PY - 2020/5/31

Y1 - 2020/5/31

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 supu∈U|M(u)f| and supu∈U|H(u)f|, when 1<p≤2. The parabolae 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 supu∈U|M(u)f| and supu∈U|H(u)f|, when 1<p≤2. The parabolae can be replaced by more general non-flat homogeneous curves.

U2 - 10.1017/S0013091519000439

DO - 10.1017/S0013091519000439

M3 - Article

VL - 63

SP - 398

EP - 412

JO - Proceedings of the Edinburgh Mathematical Society

JF - Proceedings of the Edinburgh Mathematical Society

SN - 0013-0915

IS - 2

ER -

Maximal functions associated with families of homogeneous curves: Lp bounds for p _ 2

Abstract

Access to Document

Fingerprint

Cite this