Annali di Matematica Pura ed Applicata (1923 -)

, Volume 184, Issue 3, pp 315–326

Hardy spaces H1 for Schrödinger operators with compactly supported potentials



Let L=-Δ+V be a Schrödinger operator on ℝd, d≥3, where V is a non-negative compactly supported potential that belongs to Lp for some p>d/2. Let {Kt}t>0 denote the semigroup of linear operators generated by -L. For a function f we define its H1L-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 H1L if and only if wfH1(ℝd), where H1(ℝd) is the classical real Hardy space.


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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