Arkiv för Matematik

, Volume 48, Issue 2, pp 301–310 | Cite as

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

  • Jacek Dziubański
  • Marcin PreisnerEmail author


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 fL 1(ℝ d ) for j=1,…,d, where R j =(/ x j )L −1/2 are the Riesz transforms associated with L.


Hardy Space Atomic Decomposition Perturbation Formula Classical Hardy Space Supp Versus 
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© Institut Mittag-Leffler 2010

Authors and Affiliations

  1. 1.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland
  2. 2.Instytut MatematycznyUniwersytet WrocławskiWrocławPoland

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