Let L := −Δ + V be the Schrödinger operator on ℝ n with n ≥ 3, where V is a non-negative potential satisfying Δ −1 ( V ) ∈ L ∞(ℝ n ). Let w be an L -harmonic function, determined by V , satisfying that there exists a positive constant ö such that, for any x ∈ ℝ n , 0 < δ ≤ w ( x ) ≤ 1. Assume that p (·): ℝ n → (0, 1] is a variable exponent satisfying the globally log-Hölder continuous condition. In this article, the authors show that the mappings $$H_L^{p\left( \cdot \right)}\left( {{\mathbb{R}^n}} \right)f \mapsto wf \in {H^{p\left( \cdot \right)}}\left( {{\mathbb{R}^n}} \right)$$ H L p ( ⋅ ) ( ℝ n ) ∍ f ↦ w f ∈ H p ( ⋅ ) ( ℝ n ) and $$H_L^{p\left( \cdot \right)}\left( {{\mathbb{R}^n}} \right)f \mapsto {\left( { - {\rm{\Delta }}} \right)^{1/2}}{L^{ - 1/2}}\left( f \right) \in {H^{p\left( \cdot \right)}}\left( {{\mathbb{R}^n}} \right)$$ H L p ( ⋅ ) ( ℝ n ) ∍ f ↦ ( − Δ ) 1 / 2 L − 1 / 2 ( f ) ∈ H p ( ⋅ ) ( ℝ n ) are isomorphisms between the variable Hardy spaces (ℝ n ), associated with L , and the variable Hardy spaces H p (·) (ℝ n ).

中文翻译：

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与薛定谔算子相关的可变哈代空间的同构

设 L := −Δ + V 是 ℝ n 上的薛定谔算子，其中 n ≥ 3，其中 V 是满足 Δ -1 ( V ) ∈ L ∞(ℝ n ) 的非负电势。设 w 是一个 L 谐波函数，由 V 确定，满足存在正常数 ö 使得对于任何 x ∈ ℝ n ，0 < δ ≤ w ( x ) ≤ 1。假设 p (·)： ℝ n → (0, 1] 是满足全局 log-Hölder 连续条件的变量指数。在本文中，