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Parabolic Marcinkiewicz Integrals along Surfaces on Product Domains 被引量：3

Parabolic Marcinkiewicz Integrals along Surfaces on Product Domains
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摘要 Abstract In this paper, parabolic Marcinkiewicz integral operators along surfaces on the product domain Rn ×RM （n, m ≥2） are introduced. Lp bounds of such operators are obtained under weak conditions on the kernels. Abstract In this paper, parabolic Marcinkiewicz integral operators along surfaces on the product domain Rn ×RM （n, m ≥2） are introduced. Lp bounds of such operators are obtained under weak conditions on the kernels.
作者 Ahmad AL-SALMAN
机构地区 Department of Mathematics and Statistics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第1期1-18,共18页 数学学报（英文版）
关键词 Parabolic Marcinkiewicz integral operators parabolic maximal functions Fourier transform rough kernels Parabolic Marcinkiewicz integral operators, parabolic maximal functions, Fourier transform, rough kernels
分类号 O174.2 [理学—基础数学] O175.26 [理学—基础数学]
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参考文献18

  • 1A1-Qassem, H., A1-Salman, A., Cheng, L. C., et al.: Marcinkiewicz integrals on product spaces. Studia Mathematica, 167, 227-234 (2005).
  • 2Al-Salman, A., A1-Qassem, H.: Integral operators of Marcinkiewicz type. J. Integral Equations Appl., 14(4), 343-354 (2002).
  • 3Marcinkiewicz, J.: Sur quelques integrals de type de Dini. Annales de la Societe Polonaise, 17, 42-50 (1938).
  • 4Sato, S.: Remarks on square functions in the Littlewood Paley theory. Bull. Austral. Math. Soc., 58, 199 211 (1998).
  • 5Choi, Y.: Marcinkiewicz integrals with rough homogeneous kernel of degree zero in product domains. J. Math. Anal. Appl., 261, 53-60 (2001).
  • 6Ding, Y., Fan, D., Pan, Y.: On the Lp boundedness of Marcinkiewicz integrals. Michigan. Math. J., 50, 17-26 (2002).
  • 7Ding, Y., Fan, D., Pan, Y.: Lp boundedness of Marcinkiewicz integrals with Hardy space function kernel. Acta Mathematica Sinica, English Series, 16, 593-600 (2000).
  • 8Stein, E. M.: On the functions of Littlewood-Paley, Lnsin and Marcinkiewicz. Trans. Amer. Math. Soc., 88, 430-466 (1958).
  • 9Walsh, T.: On the function of Marcinkiewicz. Studia Math., 44, 203-217 (1972).
  • 10Fabes, E., Riviere, N.: Singular integrals with mixed homogeneity. Studia Math., 27, 19-38 (1966).

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Acta Mathematica Sinica,English Series
2011年 第1期

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