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Rational Approximation of Functions in Hardy Spaces

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New Trends in Analysis and Interdisciplinary Applications

Part of the book series: Trends in Mathematics ((RESPERSP))

Abstract

We present some results on rational approximation, Laplace integral representation and Fourier spectrum characterization of functions in the Hardy Spaces. These generalize the results of Stein and Weiss in the same context for p = 2, as well as the Poisson and the Cauchy integral representation formulas for the H 2 spaces to the H p spaces on tubes for p ∈ [1, ∞]. 

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References

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Acknowledgements

This work was partially with the support of NSFC (Grant 11271045).

Author information

Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Deng Guantie

  2. Department of Mathematics, South China Agricultural University, Guangzhou, China

    Li Haichou

  3. Department of Mathematics, University of Macau, Taipa, Macau SAR, People’s Republic of China

    Qian Tao

Authors
  1. Deng Guantie
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  2. Li Haichou
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  3. Qian Tao
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Corresponding author

Correspondence to Deng Guantie .

Editor information

Editors and Affiliations

  1. Faculty of Information Technology, Macau University of Science and Technology, Taipa, Macao

    Pei Dang

  2. Department of Mathematics, University of Aveiro, Aveiro, Portugal

    Min Ku

  3. Faculty of Science and Technology, Department of Mathematics, University of Macau, Taipa, Macao

    Tao Qian

  4. Department of Mathematics, University of Torino, Torino, Italy

    Luigi G. Rodino

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Guantie, D., Haichou, L., Tao, Q. (2017). Rational Approximation of Functions in Hardy Spaces. In: Dang, P., Ku, M., Qian, T., Rodino, L. (eds) New Trends in Analysis and Interdisciplinary Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-48812-7_24

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