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Applied Mathematics and Mechanics (English Edition) ›› 2010, Vol. 31 ›› Issue (6): 761-768.doi: https://doi.org/10.1007/s10483-010-1310-z

• Articles • 上一篇    下一篇

Weighted estimates for strongly singular integral operators with rough kernels

黄文礼1 陶祥兴2 李胜宏1   

  1. 1. Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China;
    2. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, P. R. China
  • 收稿日期:2009-11-05 修回日期:2010-05-08 出版日期:2010-06-01 发布日期:2010-06-01

Weighted estimates for strongly singular integral operators with rough kernels

HUANG Wen-Li1, TAO Xiang-Xing2, LI Sheng-Hong1   

  1. 1. Department of Mathematics, Zhejiang University, Hangzhou 310027, P. R. China;
    2. Department of Mathematics, Zhejiang University of Science and Technology, Hangzhou 310023, P. R. China
  • Received:2009-11-05 Revised:2010-05-08 Online:2010-06-01 Published:2010-06-01

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摘要： The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.

关键词: strongly singular integral operators, rough kernels, Ap weights

Abstract: The Fourier transform and the Littlewood-Paley theory are used to give the weighted boundedness of a strongly singular integral operator defined in this paper. The paper shows that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.

Key words: strongly singular integral operators, rough kernels, Ap weights

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