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Annali di Matematica Pura ed Applicata (1923 -)

, Volume 184, Issue 3, pp 315–326 | Cite as

Hardy spaces H1 for Schrödinger operators with compactly supported potentials

  • Jacek DziubańskiEmail author
  • Jacek Zienkiewicz
Article

Abstract

Let L=-Δ+V be a Schrödinger operator on ℝ d , d≥3, where V is a non-negative compactly supported potential that belongs to L p for some p>d/2. Let {K t }t>0 denote the semigroup of linear operators generated by -L. For a function f we define its H1 L -norm by \(\| f\|_{H^1_L}=\| \sup_{t>0} |K_t f(x)|\|_{L^1(dx)}\). It is proved that for a properly defined weight w a function f belongs to H1 L if and only if wfH1(ℝ d ), where H1(ℝ d ) is the classical real Hardy space.

Keywords

Hardy spaces atomic decomposition Schrödinger operators 

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Copyright information

© Springer-Verlag 2004

Authors and Affiliations

  1. 1.Institute of MathematicsUniversity of WrocławWrocławPoland

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