HUANG Wen-li, TAO Xiang-xing, LI Sheng-hong. Weighted Estimates for Strongly Singular Integral Operators With Rough Kernels[J]. Applied Mathematics and Mechanics, 2010, 31(6): 731-738. doi: 10.3879/j.issn.1000-0887.2010.06.010
Citation: HUANG Wen-li, TAO Xiang-xing, LI Sheng-hong. Weighted Estimates for Strongly Singular Integral Operators With Rough Kernels[J]. Applied Mathematics and Mechanics, 2010, 31(6): 731-738. doi: 10.3879/j.issn.1000-0887.2010.06.010

Weighted Estimates for Strongly Singular Integral Operators With Rough Kernels

doi: 10.3879/j.issn.1000-0887.2010.06.010
  • Received Date: 2009-10-27
  • Rev Recd Date: 2010-05-11
  • Publish Date: 2010-06-15
  • The Fourier trans form and Little wood-Paley theory were used to give the weighted boundedness of the strongly singular in tegraloperator. It is shown that the strongly singular integral operator is bounded from the Sobolev space to the Lebesgue space.
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  • [1]
    Caldern A P, Zygmund A. On singular integrals[J]. Amer J Math, 1956, 78(2):289-309. doi: 10.2307/2372517
    [2]
    Fefferman R. A note on singular integrals[J]. Proc Amer Math Soc, 1979, 74(2):266-270. doi: 10.1090/S0002-9939-1979-0524298-3
    [3]
    Duoandikoetxea J, Rubio De Francia J L. Maximal and singular integral operators via Fourier transform estimates [J].Invent Math, 1986, 84(3):541-561. doi: 10.1007/BF01388746
    [4]
    Fan D,Pan Y. Singular integral operators with rough kernels supported by subvarieties[J]. Amer J Math, 1997, 119:799-839. doi: 10.1353/ajm.1997.0024
    [5]
    Chen J C, Fan D S, Ying Y M. Certain operators with rough singular kernels[J]. Canad J Math, 2003, 55(3): 504-532. doi: 10.4153/CJM-2003-021-4
    [6]
    Chen Q L, Zhang Z F. Boundedness of a class of super singular integral operators and the associated commutators[J].Science in China A, 2004 ,47(6): 842-853.
    [7]
    Xia X. Boundedness of strongly singular integral operators with rough kernels[J]. Journal of Beijing Normal University, 2007, 43(1):10-15.
    [8]
    Chen Q L. Weighted estimates for a class of rough singular integrals [J]. Journal of Zhejiang University, 2004, 31(5):481-483.
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