| 陈杰诚,李艳诘.沿平坦凸曲线Hilbert变换的L2有界性[J].数学年刊A辑,2020,41(2):221~232 |
| 沿平坦凸曲线Hilbert变换的L2有界性 |
| L2 Boundedness of Hilbert Transform Along Convex Flat Curves |
| Received:April 06, 2016 Revised:January 05, 2017 |
| DOI：10.16205/j.cnki.cama.2020.0016 |
| 中文关键词: Hilbert变换, 双倍条件, 震荡积分 |
| 英文关键词:Hilbert transform, Doubling condition, Oscillatory integral |
| 基金项目:国家自然科学基金(No.\,11471288, No.\,11671363)和浙江省自然科学基金(No. LY14A010015) |
| Author Name | Affiliation | | CHEN Jiecheng | Department of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, China. | | LI Yanjie | Department of Mathematics, Physics and Information Engineering, Zhejiang Normal University, Jinhua 321004, Zhejiang, China. |
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| 中文摘要: |
| 考虑一类平坦凸曲线的Hilbert变换H_\gamma f(x)=\texttt{p.v.}\int_{-\infty}^{+\infty}f(x_1-t,x_2-\gamma(t))\frac{\rmd t}{t},\quad \forall x:=(x_1,x_2)\in \mathbb{R}^2.对于平坦凸曲线, 给出H_{\gamma}是L^2有界的一些必要条件. |
| 英文摘要: |
| The authors consider the Hilbert transform along a convex flat curve in mathbb{R}^2:H_\gamma f(x)=\texttt{p.v.}\int_{-\infty}^{+\infty} f(x_1-t,x_2-\gamma(t))\frac{\rmd t}{t},\quad \forall x:=(x_1,x_2)\in \mathbb{R}^2.They give some necessary conditions such that H_\gamma is bounded on L^2 for convex flat curves. |
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