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.

引用

页数：36

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