加权Hardy空间上Schr dinger算子的里斯变换
Riesz transforms associated with Schrödinger operators acting on weighted Hardy spaces
摘要：
设$L=-Δ+V$是作用在$L^2(\mathbb R^n)$上的薛定谔算子$n\ge1$，其中$V\not\equiv 0$是$\mathbb R^n$上的非负局部可积函数.本文利用面积积分函数引入与$L$相联系的加权Hardy空间$H^p_L(w)$，并研究其原子分解理论.我们还证明了当$\frac{n}{n+1}<p<1$和$w\in A_1\cap RH_{(2/p)'}$满足时，与$L$相关的Riesz变换$\nabla L^{-1/2}$从我们的新空间$H^p_L(w)$到经典加权Hardy空间$H^p(w)$是有界的.
英文摘要：
Let $L=-Δ+V$ be a Schrödinger operator acting on $L^2(\mathbb R^n)$, $n\ge1$, where $V\not\equiv 0$ is a nonnegative locally integrable function on $\mathbb R^n$. In this article, we will introduce weighted Hardy spaces $H^p_L(w)$ associated with $L$ by means of the area integral function and study their atomic decomposition theory. We also show that the Riesz transform $\nabla L^{-1/2}$ associated with $L$ is bounded from our new space $H^p_L(w)$ to the classical weighted Hardy space $H^p(w)$ when $\frac{n}{n+1}<p<1$ and$w\in A_1\cap RH_{(2/p)'}$.
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