Endpoint estimates for Riesz transforms of magnetic Schrödinger operators

Xuan Thinh Duong Department of Mathematics, Macquarie University El Maati Ouhabaz Laboratoire Bordelais d’Analyse et Geometrie, C.N.R.S. UMR 5467 Universite Bordeaux 1 Lixin Yan Department of Mathematics, Macquarie University

TBD mathscidoc:1701.333086

Arkiv for Matematik, 44, (2), 261-275, 2005.6
Let $A=-(\nabla-i\vec{a})^2+V$ be a magnetic Schrödinger operator acting on$L$^{2}($R$^{$n$}),$n$≥1, where $\vec{a}=(a_1,\cdots,a_n)\in L^2_{\rm loc}$ and 0≤$V$∈$L$^{1}_{loc}. Following [1], we define, by means of the area integral function, a Hardy space$H$^{1}_{$A$}associated with$A$. We show that Riesz transforms (∂/∂$x$_{$k$}-$i$$a$_{$k$})$A$^{-1/2}associated with$A$, $k=1,\cdots,n$ , are bounded from the Hardy space$H$^{1}_{$A$}into$L$^{1}. By interpolation, the Riesz transforms are bounded on$L$^{$p$}for all 1<$p$≤2.
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@inproceedings{xuan2005endpoint,
  title={Endpoint estimates for Riesz transforms of magnetic Schrödinger operators},
  author={Xuan Thinh Duong, El Maati Ouhabaz, and Lixin Yan},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203617622402895},
  booktitle={Arkiv for Matematik},
  volume={44},
  number={2},
  pages={261-275},
  year={2005},
}
Xuan Thinh Duong, El Maati Ouhabaz, and Lixin Yan. Endpoint estimates for Riesz transforms of magnetic Schrödinger operators. 2005. Vol. 44. In Arkiv for Matematik. pp.261-275. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20170108203617622402895.
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