数学物理学报 ›› 2011, Vol. 31 ›› Issue (1): 76-81.

• 论文 • 上一篇    下一篇

齐次超曲面上测度Fourier变换的平均衰减估计

程美芳1, 张震球2   

  1. 1.安徽师范大学数学计算机科学学院 安徽芜湖 241000|2.南开大学数学学院 天津 300071
  • 收稿日期:2008-05-08 修回日期:2009-12-15 出版日期:2011-02-25 发布日期:2011-02-25
  • 基金资助:

    国家自然科学基金(10671041, 10971039)和安徽省教育厅一般项目(KJ2008B244)资助

Average Decay Estimates for Fourier Transforms of Measure Supported on Homogeneous Hypersurfaces

 CHENG Mei-Fang1, ZHANG Zhen-Qiu2   

  1. 1.College of Mathematics and Computer Sciences, Anhui Normal University, Anhui Wuhu 241000|2.School of Mathematical Sciences, Nankai University, Tianjin 300071
  • Received:2008-05-08 Revised:2009-12-15 Online:2011-02-25 Published:2011-02-25
  • Supported by:

    国家自然科学基金(10671041, 10971039)和安徽省教育厅一般项目(KJ2008B244)资助

摘要:

该文主要考虑限制在齐次超曲面上的测度dμ的Fourier变换的Lq范数估计. 基于此结论, 还得到了一些有关卷积算子Tf(x, θ)=f * μθ(x)的混合范数不等式.

关键词: Fourier变换, 混合范数, 齐次超曲面

Abstract:

In this paper, the authors consider average decay estimates for the Fourier transform μ of densities supported on a homogeneous hypersurface. Based on these results, the authors also obain some mixed-norm inequalities for the convolution operator defined by
Tf(xθ)=f *μθ(x), where μθ(x) is the rotation measure.

Key words: Fourier transform, Mixed-norm, Homogeneous hypersurface

中图分类号: 

  • 42B20