Approximation Theory and its Applications

, Volume 7, Issue 2, pp 106–117 | Cite as

The group Fourier transforms and multipiers of the Hardy spaces on the Heisenberg group

  • Liu Heping


We give the estimate for the growth of the group Fourier transforms of the Hardy spaces and establish and Hp-multipleir theorem satisfying Michlin condition on the Heisenberg group.


Bounded Operator Hardy Space Heisenberg Group Homogeneous Degree Laguerre Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Folland, G.B. and Stein, E.M., Estimates for the ∂b Complex and Analysis on the Heisenberg Group, Comm. Pure. Appl. Math. 27 (1974), 427–522.CrossRefMathSciNetGoogle Scholar
  2. [2]
    Folland, G.B. and Stein, E.M., Hardy Spaces on Homonegeous Groups, Princeton Univ. Press and Univ. Tokyo Press, Princeton, 1982.Google Scholar
  3. [3]
    Geller, D., Fourier Analysis on the Heisenberg-Group I, Schwartz Space, J. Func. Anal. 36 (1980), 205–254.MATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    Hemler, M.L., The Molecular Theory ofH p,q,r(Hn), Ph.D. Dissertation, Washington Univ., St. Louis, 1980.Google Scholar
  5. [5]
    Latter, R.H. and Uchiyama, A., The Atomic Decomposition for ParabolicH p Spaces, Trans. Amer. Math. Soc. 253 (1979), 391–398.MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Mauceri, G., Zonal Multipliers on the Heisenberg Group, Pacific J. Math. 95 (1981), 143–159.MATHMathSciNetGoogle Scholar
  7. [7]
    Michele, L. and Mauceri, G.,L p-multipliers on the Heisenberg Group, Proc. Symp. in Pure Math. 35 (1979), 355–359.Google Scholar
  8. [8]
    Stein, E.M., Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, New Jersey, 1970.MATHGoogle Scholar
  9. [9]
    Taibleson, M.H. and Weiss, G., The Molecular Characterization of Certain Hardy Spaces, Astersque 77 (1980), 68–149.Google Scholar

Copyright information

© Springer 1991

Authors and Affiliations

  • Liu Heping
    • 1
  1. 1.Department of MathematicsBeijing Normal UniversityBeijingPRC

Personalised recommendations