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
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.
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页码:69 / 114
页数:46
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