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 \(H_A^{p\left(\cdot \right)}\left({{\mathbb{R}^n}} \right)\) 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 \(H_A^{p\left(\cdot \right)}\left({{\mathbb{R}^n}} \right)\) to L^p(·)(ℝⁿ) or from \(H_A^{p\left(\cdot \right)}\left({{\mathbb{R}^n}} \right)\) to itself.

设A是上ℝ一个膨胀扩张^Ñ，和p（·）：ℝ ^ñ →（0，∞）是满足全局登录持有人连续状态的变量指数函数。令\（H_A ^ {p \ left（\ cdot \ right）} \ left（{{\ mathbb {R} ^ n}} \ right）\）是通过非切向盛大极大函数定义的各向异性各向异性Hardy空间。在本文中，作者建立了它的分子分解，即使在经典的各向同性环境下（在A：= 2I _n×n的情况下），它仍然是新的。作为应用程序，作者从\（H_A ^ {p \ left（\ cdot \ right）} \ left（{{\\ mathbb {R} ^ n}} \ right）\）到各向异性Calderon-Zygmund算子的有界性大号^p（·）（ℝ ^ñ）或从\（H_A ^ {P \左（\ CDOT \右）} \左（{{\ mathbb {R} ^ N}} \右）\）到其自身。