# MathSciDoc: An Archive for Mathematician ∫

#### TBDmathscidoc:1701.333175

Arkiv for Matematik, 48, (2), 301-310, 2009.2
Let$L$=−Δ+$V$be a Schrödinger operator on ℝ^{$d$},$d$≥3. We assume that$V$is a nonnegative, compactly supported potential that belongs to$L$^{$p$}(ℝ^{$d$}), for some$p$>$d$$/2. LetK_{t}be the semigroup generated by −L. We say that anL^{1}(ℝ^{d})-functionfbelongs to the Hardy space H^{1}_{L} associated withLif sup_{t>0}|K_{t}f| belongs toL^{1}(ℝ^{d}). We prove that f\in H^{1}_{L} if and only ifR_{j}f∈L^{1}(ℝ^{d}) forj=1,…,d, whereR_{j}=(∂/∂$$x$_{$j$})$L$^{−1$/$2}are the Riesz transforms associated with$L$.
@inproceedings{jacek2009riesz,
title={Riesz transform characterization of Hardy spaces associated with Schrödinger operators with compactly supported potentials},
author={Jacek Dziubański, and Marcin Preisner},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203627986815984},
booktitle={Arkiv for Matematik},
volume={48},
number={2},
pages={301-310},
year={2009},
}

Jacek Dziubański, and Marcin Preisner. Riesz transform characterization of Hardy spaces associated with Schrödinger operators with compactly supported potentials. 2009. Vol. 48. In Arkiv for Matematik. pp.301-310. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203627986815984.