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Bilinear Pseudo-differential Operators on Local Hardy Spaces 被引量：2

Bilinear Pseudo-differential Operators on Local Hardy Spaces
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摘要 In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type （1, 0） in the sense of HSrmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces. In this paper, the authors consider a class of bilinear pseudo-differential operators with symbols of order 0 and type （1, 0） in the sense of HSrmander and use the atomic decompositions of local Hardy spaces to establish the boundedness of the bilinear pseudo-differential operators and the bilinear singular integral operators on the product of local Hardy spaces.
作者 Jiang Wei XIAO Yin Sheng JIANG Wen Hua GAO
机构地区 College of Mathematics and Systems Science School of Appied Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2012年第2期255-266,共12页 数学学报（英文版）
基金 supported by National Natural Science Foundation of China(Grant No.10861010)
关键词 Bilinear pseudo-differential operators local Hardy spaces singular integrals Bilinear pseudo-differential operators, local Hardy spaces, singular integrals
分类号 O175.3 [理学—基础数学]
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参考文献10

  • 1Fefferman, C., Stein, E. M.: Hp spaces of several variables. Acta Math., 129, 137-193 (1972).
  • 2Goldberg, D.: A local version of real Hardy spaces. Duke Math. J., 46, 27-42 (1979).
  • 3Coifman, R., Weiss, G.: Extensions of Hardy spaces and their use in analysis. Bull. Amer. Math. Soc., 83, 569-645 (1977).
  • 4Hormander, L.: Pseudodifferential operators and hypoelliptic equations. Proc. Symp. Pure Math., 10, 138 -183 (1967).
  • 5Benyi, A., Torres, R. H.: Symbolic calculus and the transposes of bilinear pseudodifferential operators. Comm. Par. Diff. Eq., 28, 1161-1181 (2003).
  • 6Grafakos, L., Torres, R. H.: Multilinear Calderon-Zygmund theory. Adv. Math., 165, 124-164 (2002).
  • 7Maldonado, D., Naibo, V.: Weighted norm inequalities for paraproducts and bilinear pseudo-differential operators with mild regularity. J. Fourier Anal. Appl., 15. 218-261 (2009).
  • 8Grafakos, L., Kalton, N.: Multilinear Calderon-Zygmund operators on Hardy spaces. Collect. Math., 52, 169-179 (2001).
  • 9Lin, Y., Lu, S. Z.: Boundedness of multilinear singular integral operators on Hardy and Herz-type spaces. Hokkaido Math. J., 36, 585-613 (2007).
  • 10Stein, E. M.: Harmonic Analysis: Real-Variable Methods, OrthogonMity, and Oscillatory Integrals, Prince- ton University Press, Princeton, 1993.

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Acta Mathematica Sinica,English Series
2012年 第2期

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