Riesz transform characterization of Hardy spaces associated with Schrödinger operators with compactly supported potentials

Jacek Dziubański Instytut Matematyczny, Uniwersytet Wrocławski Marcin Preisner Instytut Matematyczny, Uniwersytet Wrocławski

TBD mathscidoc: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$$/$2. Let$K$_{$t$}be the semigroup generated by −$L$. We say that an$L$^{1}(ℝ^{$d$})-function$f$belongs to the Hardy space $H^{1}_{L}$ associated with$L$if sup_{$t$>0}|$K$_{$t$}$f$| belongs to$L$^{1}(ℝ^{$d$}). We prove that $f\in H^{1}_{L}$ if and only if$R$_{$j$}$f$∈$L$^{1}(ℝ^{$d$}) for$j$=1,…,$d$, where$R$_{$j$}=($∂$/$∂$$x$_{$j$})$L$^{−1$/$2}are the Riesz transforms associated with$L$.
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@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.
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