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

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Approximation Theory and its Applications

Abstract

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.

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References

  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.

    Article  MathSciNet  Google Scholar 

  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. Geller, D., Fourier Analysis on the Heisenberg-Group I, Schwartz Space, J. Func. Anal. 36 (1980), 205–254.

    Article  MATH  MathSciNet  Google Scholar 

  4. Hemler, M.L., The Molecular Theory ofH p,q,r(Hn), Ph.D. Dissertation, Washington Univ., St. Louis, 1980.

    Google Scholar 

  5. Latter, R.H. and Uchiyama, A., The Atomic Decomposition for ParabolicH p Spaces, Trans. Amer. Math. Soc. 253 (1979), 391–398.

    Article  MATH  MathSciNet  Google Scholar 

  6. Mauceri, G., Zonal Multipliers on the Heisenberg Group, Pacific J. Math. 95 (1981), 143–159.

    MATH  MathSciNet  Google Scholar 

  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. Stein, E.M., Singular Integrals and Differentiability Properties of Functions, Princeton Univ. Press, Princeton, New Jersey, 1970.

    MATH  Google Scholar 

  9. Taibleson, M.H. and Weiss, G., The Molecular Characterization of Certain Hardy Spaces, Astersque 77 (1980), 68–149.

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Beijing Normal University, 100875, Beijing, PRC

    Liu Heping

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  1. Liu Heping
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Heping, L. The group Fourier transforms and multipiers of the Hardy spaces on the Heisenberg group. Approx. Theory & its Appl. 7, 106–117 (1991). https://doi.org/10.1007/BF02845195

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  • DOI: https://doi.org/10.1007/BF02845195

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