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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

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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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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

2010 MSC Number: 

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