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Maximal Function Characterizations of Hardy Spaces on R n with Pointwise Variable Anisotropy

Author

Listed:
  • Aiting Wang

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
    College of Mathematics and Statistics, Qinghai Minzu University, Xining 810007, China
    These authors contributed equally to this work.)

  • Wenhua Wang

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
    These authors contributed equally to this work.)

  • Baode Li

    (College of Mathematics and System Science, Xinjiang University, Urumqi 830017, China
    These authors contributed equally to this work.)

Abstract

In 2011, Dekel et al. developed highly geometric Hardy spaces H p ( Θ ) , for the full range 0 < p ≤ 1 , which were constructed by continuous multi-level ellipsoid covers Θ of R n with high anisotropy in the sense that the ellipsoids can rapidly change shape from point to point and from level to level. In this article, when the ellipsoids in Θ rapidly change shape from level to level, the authors further obtain some real-variable characterizations of H p ( Θ ) in terms of the radial, the non-tangential, and the tangential maximal functions, which generalize the known results on the anisotropic Hardy spaces of Bownik.

Suggested Citation

  • Aiting Wang & Wenhua Wang & Baode Li, 2021. "Maximal Function Characterizations of Hardy Spaces on R n with Pointwise Variable Anisotropy," Mathematics, MDPI, vol. 9(24), pages 1-19, December.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:24:p:3246-:d:702853
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