A maximal function for families of Hilbert transforms along homogeneous curves

被引：7

作者：

Guo, Shaoming ^{[1
]}

Roos, Joris ^{[1
]}

Seeger, Andreas ^{[1
]}

Yung, Po-Lam ^{[2
]}

机构：

[1] Univ Wisconsin, Dept Math, 480 Lincoln Dr, Madison, WI 53706 USA

[2] Chinese Univ Hong Kong, Dept Math, Shatin, Hong Kong, Peoples R China

来源：

MATHEMATISCHE ANNALEN | 2020年 / 377卷 / 1-2期

基金：

英国工程与自然科学研究理事会; 美国国家科学基金会;

关键词：

SINGULAR-INTEGRALS; HARMONIC-ANALYSIS; OPERATORS; INEQUALITIES;

D O I：

10.1007/s00208-019-01915-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let H-(u) be the Hilbert transform along the parabola (t, ut(2)) where u is an element of R. For a set U of positive numbers consider the maximal function H-U f = sup{vertical bar H-(u) f vertical bar : u is an element of U}. We obtain an (essentially) optimal result for the L-p operator norm of H-U when 2 < p < infinity. The results are proved for families of Hilbert transforms along more general nonflat homogeneous curves.

引用

页码：69 / 114

页数：46

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