A maximal function for families of Hilbert transforms along homogeneous curves

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

doi:10.1007/s00208-019-01915-3

A maximal function for families of Hilbert transforms along homogeneous curves

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

School of Mathematics

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Abstract / Description of output

Let H(u) be the Hilbert transform along the parabola (t,ut2) where u∈R. For a set U of positive numbers consider the maximal function HUf=sup{|H(u)f|:u∈U}. We obtain an (essentially) optimal result for the Lp operator norm of HU when 2<p<∞. The results are proved for families of Hilbert transforms along more general nonflat homogeneous curves.

Original language	English
Pages (from-to)	69–114
Number of pages	44
Journal	Mathematische annalen
Volume	377
Early online date	17 Oct 2019
DOIs	https://doi.org/10.1007/s00208-019-01915-3
Publication status	Published - 30 Jun 2020

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10.1007/s00208-019-01915-3

1902.00096Accepted author manuscript, 431 KB

https://arxiv.org/abs/1902.00096

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title = "A maximal function for families of Hilbert transforms along homogeneous curves",

abstract = "Let H(u) be the Hilbert transform along the parabola (t,ut2) where u∈R. For a set U of positive numbers consider the maximal function HUf=sup{|H(u)f|:u∈U}. We obtain an (essentially) optimal result for the Lp operator norm of HU when 2<p<∞. The results are proved for families of Hilbert transforms along more general nonflat homogeneous curves.",

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AU - Guo, Shaoming

AU - Roos, Joris

AU - Seeger, Andreas

AU - Yung, Po-Lam

PY - 2020/6/30

Y1 - 2020/6/30

N2 - Let H(u) be the Hilbert transform along the parabola (t,ut2) where u∈R. For a set U of positive numbers consider the maximal function HUf=sup{|H(u)f|:u∈U}. We obtain an (essentially) optimal result for the Lp operator norm of HU when 2<p<∞. The results are proved for families of Hilbert transforms along more general nonflat homogeneous curves.

AB - Let H(u) be the Hilbert transform along the parabola (t,ut2) where u∈R. For a set U of positive numbers consider the maximal function HUf=sup{|H(u)f|:u∈U}. We obtain an (essentially) optimal result for the Lp operator norm of HU when 2<p<∞. The results are proved for families of Hilbert transforms along more general nonflat homogeneous curves.

U2 - 10.1007/s00208-019-01915-3

DO - 10.1007/s00208-019-01915-3

M3 - Article

SN - 0025-5831

VL - 377

SP - 69

EP - 114

JO - Mathematische annalen

JF - Mathematische annalen

ER -

A maximal function for families of Hilbert transforms along homogeneous curves

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