Molecular Decomposition of Anisotropic Hardy Spaces With Variable Exponents

Let A be an expansive dilation on ℝ n , and p (·): ℝ n → (0, ∞) be a variable exponent function satisfying the globally log-Holder continuous condition. Let 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 := 2I n×n ). As applications, the authors obtain the boundedness of anisotropic Calderon-Zygmund operators from H A p ( ⋅ ) ( ℝ n ) to L p (·) (ℝ n ) or from H A p ( ⋅ ) ( ℝ n ) to itself.