Abstract
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 {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 wf∈H1(ℝd), where H1(ℝd) is the classical real Hardy space.
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Mathematics Subject Classification (2000)
42B30, 35J10, 42B25
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Dziubański, J., Zienkiewicz, J. Hardy spaces H1 for Schrödinger operators with compactly supported potentials. Annali di Matematica 184, 315–326 (2005). https://doi.org/10.1007/s10231-004-0116-6
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DOI: https://doi.org/10.1007/s10231-004-0116-6