Acta mathematica scientia,Series A ›› 2011, Vol. 31 ›› Issue (1): 76-81.

• Articles • Previous Articles     Next Articles

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

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

CLC Number: 

  • 42B20
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