Riesz Transforms Associated with Schrödinger Operators Acting on Weighted Hardy Spaces (Analysis in Theory and Applications, 2017)
Let $L = −∆+V$ be a Schrödinger operator acting on $L^2(\mathbb{R}^n)$, $n ≥ 1$, where $V ot\equiv 0$ is a nonnegative locally integrable function on $\mathbb{R}^n$. In this article, we will introduceweighted Hardy spaces $H^p_L(w)$ associated with $L$ by means of the square functionand then study their atomic decomposition theory. We will also show that the Riesztransform $∇L^{−1/2}$ associated with $L$ is bounded from our new space $H^p_L (w)$ to theclassical weighted Hardy space $H^p(w)$ when $n/(n+1)< p