Year: 2015
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 2 : pp. 138–153
Abstract
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 $H^p_L (w)$ to the classical weighted Hardy space $H^p(w)$ when $n/(n+1)< p<1$ and $w ∈ A_1∩RH_{(2/p)′}$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/ata.2015.v31.n2.4
Analysis in Theory and Applications, Vol. 31 (2015), Iss. 2 : pp. 138–153
Published online: 2015-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Weighted Hardy space Riesz transform Schrödinger operator atomic decomposition $A_p$ weight.
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The Boundedness of Some Integral Operators on Weighted Hardy Spaces Associated with Schrödinger Operators
Wang, Hua
Journal of Function Spaces, Vol. 2015 (2015), Iss. P.1
https://doi.org/10.1155/2015/823862 [Citations: 0]