Riesz transforms associated with Schrödinger operators acting on weighted Hardy spaces

Details Riesz transforms associated with Schrödinger operators acting on weighted Hardy spaces Riesz transforms associated with Schrödinger operators acting on weighted Hardy spaces

2011-02-27

arxiv.org/abs/1102.5467v1

Mathematics

Classical Analysis and ODEs

17 pages

Scientific paper

Let $L=-\Delta+V$ be a Schr\"odinger 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}

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