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L^p(R^m× R^n) boundedness for the Marcinkiewicz integral on product spaces 被引量:7

L^p(R^m× R^n) boundedness for the Marcinkiewicz integral on product spaces
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摘要 Lp(Rm × Rn) boundedness is considered for the multiple Marcinkiewicz integral. Some sizeconditions implying the Lp(Rm × Rn) boundedness of the multiple Marcinkiewicz integral for some fixed1 < p <∞ are obtained. Lp(Rm × Rn) boundedness is considered for the multiple Marcinkiewicz integral. Some size conditions implying the LP(Rm × Rn) boundedness of the multiple Marcinkiewicz integral for some fixed 1 < p <∞ are obtained.
出处 《Science China Mathematics》 SCIE 2003年第1期75-82,共8页 中国科学:数学(英文版)
基金 This work was supported by the NSF of Henan Province, National 973 Project ofChina (G19990751) Prof. Xu Yuesheng's research grant in the program of "One Hundred Distinguished Young Scientists" of the Chinese Academy of Sciences.
关键词 multiple MARCINKIEWICZ integral FOURIER transform estimate LITTLEWOOD-PALEY theory. multiple Marcinkiewicz integral, Fourier transform estimate, Littlewood-Paley the-ory.
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  • 1Stein,E. M.On the functions of Littlewood-Paley, Lusin, and Marcinkiewicz, Trams[].Journal of the American Mathematical Society.1958
  • 2Stein,E. M.Singular Integrals and Differentiability Properties of Functions, New Jersey: Princeton Univ[]..1970

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