Molecular Decomposition of Anisotropic Hardy Spaces With Variable Exponents

Wenhua Wang (), Xiong Liu (), Aiting Wang () and Baode Li ()
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Wenhua Wang: Xinjiang University
Xiong Liu: Xinjiang University
Aiting Wang: Xinjiang University
Baode Li: Xinjiang University

Indian Journal of Pure and Applied Mathematics, 2020, vol. 51, issue 4, 1471-1495

Abstract: Abstract Let A be an expansive dilation on ℝn, and p(·): ℝn → (0, ∞) be a variable exponent function satisfying the globally log-Holder continuous condition. Let $$H_A^{p\left(\cdot \right)}\left({{\mathbb{R}^n}} \right)$$ H A p ( ⋅ ) ( ℝ n ) be the variable anisotropic Hardy space defined via the non-tangential grand maximal function. In this paper, the authors establish its molecular decomposition, which is still new even in the classical isotropic setting (in the case A:= 2In×n). As applications, the authors obtain the boundedness of anisotropic Calderon-Zygmund operators from $$H_A^{p\left(\cdot \right)}\left({{\mathbb{R}^n}} \right)$$ H A p ( ⋅ ) ( ℝ n ) to Lp(·)(ℝn) or from $$H_A^{p\left(\cdot \right)}\left({{\mathbb{R}^n}} \right)$$ H A p ( ⋅ ) ( ℝ n ) to itself.

Keywords: Anisotropy; Hardy space; molecule; Calderon-Zygmund operator; 42B20; 42B30; 46E30 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1007/s13226-020-0477-6

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