TY - JOUR
T1 - Riesz Transforms Associated with Schrödinger Operators Acting on Weighted Hardy Spaces
JO - Analysis in Theory and Applications
VL - 2
SP - 138
EP - 153
PY - 2017
DA - 2017/04
SN - 31
DO - http://doi.org/10.4208/ata.2015.v31.n2.4
UR - https://global-sci.org/intro/article_detail/ata/4629.html
KW - Weighted Hardy space, Riesz transform, Schrödinger operator, atomic decomposition, $A_p$ weight.
AB - <p style="text-align: justify;">Let $L = −∆+V$ be a Schrödinger operator acting on $L^2(\mathbb{R}^n)$, $n ≥ 1$, 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 square function
and then study their atomic decomposition theory. We will also show that the Riesz
transform $∇L^{−1/2}$ associated with $L$ is bounded from our new space $H^p_L&nbsp;(w)$ to the
classical weighted Hardy space $H^p(w)$ when $n/(n+1)&lt; p&lt;1$ and $w ∈ A_1∩RH_{(2/p)′}$.</p>