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The boundedness of higher order Riesz transform associated with Sch
SHEN Jian-Chun,Dong Jianfeng
Department of Mathematics, School of Science, Shanghai University, Shanghai 200444
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Funding: none
Opened online: 9 January 2015
Accepted by: none
Citation: SHEN Jian-Chun,Dong Jianfeng.The boundedness of higher order Riesz transform associated with Sch[OL]. [ 9 January 2015] http://en.paper.edu.cn/en_releasepaper/content/4626619
 
 
Let $L=-Delta+V$ be a Schr"{o}dinger operator on $mathbb{R}^n$ ($n geq 3$) , where $V ot equiv 0$ is a nonnegative potential belonging to certain reverse H"{o}lder class $B_s$ for $s geq n$. The Hardy type spaces $H_L^p, rac{n}{n+delta}<pleq 1$ for some $delta >0$, are defined in terms of the maximal function with respect to the semigroup ${e^{-tL} }_{t>0}$. In this article, we investigate the boundedness of some integral operator related to $L$, such as $VL^{-1}$, $Delta L^{-1}$ and $ abla^2 L^{-1}$, on spaces $H_L^p(mathbb{R}^n)$.
Keywords:Hardy space; molecule;reverse H\"{o}lder class;Schrodinger operator;Riesz transform
 
 
 

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