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Molecular Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications

Author

Listed:
  • Jun Liu

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China)

  • Long Huang

    (School of Mathematics and Information Science, Key Laboratory of Mathematics and Interdisciplinary Sciences of the Guangdong Higher Education Institute, Guangzhou University, Guangzhou 510006, China)

  • Chenlong Yue

    (School of Mathematics, China University of Mining and Technology, Xuzhou 221116, China)

Abstract

Let p → ∈ ( 0 , ∞ ) n be an exponent vector and A be a general expansive matrix on R n . Let H A p → ( R n ) be the anisotropic mixed-norm Hardy spaces associated with A defined via the non-tangential grand maximal function. In this article, using the known atomic characterization of H A p → ( R n ) , the authors characterize this Hardy space via molecules with the best possible known decay. As an application, the authors establish a criterion on the boundedness of linear operators from H A p → ( R n ) to itself, which is used to explore the boundedness of anisotropic Calderón–Zygmund operators on H A p → ( R n ) . In addition, the boundedness of anisotropic Calderón–Zygmund operators from H A p → ( R n ) to the mixed-norm Lebesgue space L p → ( R n ) is also presented. The obtained boundedness of these operators positively answers a question mentioned by Cleanthous et al. All of these results are new, even for isotropic mixed-norm Hardy spaces on R n .

Suggested Citation

  • Jun Liu & Long Huang & Chenlong Yue, 2021. "Molecular Characterizations of Anisotropic Mixed-Norm Hardy Spaces and Their Applications," Mathematics, MDPI, vol. 9(18), pages 1-24, September.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:18:p:2216-:d:632487
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    References listed on IDEAS

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    1. A. G. Georgiadis & M. Nielsen, 2016. "Pseudodifferential operators on mixed-norm Besov and Triebel–Lizorkin spaces," Mathematische Nachrichten, Wiley Blackwell, vol. 289(16), pages 2019-2036, November.
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