Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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DUALITIES OF VARIABLE ANISOTROPIC HARDY SPACES AND BOUNDEDNESS OF SINGULAR INTEGRAL OPERATORS

  • Wang, Wenhua (School of Mathematics and Statistics Wuhan University)
  • Received : 2020.04.02
  • Accepted : 2020.09.15
  • Published : 2021.03.31
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Abstract

Let A be an expansive dilation on ℝn, and p(·) : ℝn → (0, ∞) be a variable exponent function satisfying the globally log-Hölder continuous condition. Let Hp(·)A (ℝn) be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the author obtains the boundedness of anisotropic convolutional ��-type Calderón-Zygmund operators from Hp(·)A (ℝn) to Lp(·) (ℝn) or from Hp(·)A (ℝn) to itself. In addition, the author also obtains the duality between Hp(·)A (ℝn) and the anisotropic Campanato spaces with variable exponents.

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References

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