Hilbert transforms along variable planar curves: Lipschitz regularity

被引：2
|
作者：
Liu, Naijia [1 ]
Yu, Haixia [2 ]
机构：
[1] Sun Yat Sen Univ, Dept Math, Guangzhou 510275, Guangdong, Peoples R China
[2] Shantou Univ, Dept Math, Shantou 515063, Peoples R China
来源：
JOURNAL OF FUNCTIONAL ANALYSIS | 2022年 / 282卷 / 04期
关键词：
Hilbert transform; Variable curve; Square function estimate; Local smoothing estimate; SINGULAR RADON TRANSFORMS; MAXIMAL FUNCTIONS; INEQUALITIES; OPERATORS;
D O I：
10.1016/j.jfa.2021.109340
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we obtain the L-p-boundedness of the Hilbert transform H-gamma for 1 < p < infinity along a variable plane curve (t, u( x(1), x(2))gamma(t)), where uis a Lipschitz function with small Lipschitz norm, and gamma is a general curve satisfying some suitable smoothness and curvature conditions. (c) 2021 Elsevier Inc. All rights reserved.
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页数：36
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