与薛定谔算子相关的加权局部Hardy空间
Weighted local Hardy spaces associated to Schrödinger operators
摘要：
本文利用局部垂直极大函数、局部非切极大函数和原子分解刻画了与临界半径函数$ρ$和权$ω\in A_{\infty}^{ρ,\,\infty}(\mathbb{R}^{n})$相关的加权局部Hardy空间$h^p_ρ(ω)$，这些权在局部表现为Muckenhoupt权，并且实际上包含了它们.通过原子刻画，我们还证明了与$h^{p}_ρ(ω)$相关的有限原子分解的存在性。进一步，我们建立了拟Banach值次线性算子在$h^p_ρ(ω)$中的有界性.作为它们的应用，我们建立了与薛定谔算子$\cal L$和$ω\in A_1^{ρ,\infty}(\mathbb{R}^{n})$相关的加权局部Hardy空间$h^1_ρ(ω)$和加权Hardy空间$H^1_{\cal L}(ω)$的等价性
英文摘要：
In this paper, we characterize the weighted local Hardy spaces $h^p_ρ(ω)$ related to the critical radius function $ρ$ and weights $ω\in A_{\infty}^{ρ,\,\infty}(\mathbb{R}^{n})$ which locally behave as Muckenhoupt's weights and actually include them, by the local vertical maximal function, the local nontangential maximal function and the atomic decomposition. By the atomic characterization, we also prove the existence of finite atomic decompositions associated with $h^{p}_ρ(ω)$. Furthermore, we establish boundedness in $h^p_ρ(ω)$ of quasi- Banach-valued sublinear operators. As their applications, we establish the equivalence of the weighted local Hardy space $h^1_ρ(ω)$ and the weighted Hardy space $H^1_{\cal L}(ω)$ associated to Schrödinger operators $\cal L$ with $ω\in A_1^{ρ,\infty}(\mathbb{R}^{n})$
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